ALBERT

Description: An inherent numerical problem associated with the fully explicit pseudospectral numerical simulation of the incompressible Navier-Stokes equation for viscous flows with no-slip walls is described. A semi-implicit scheme which circumvents this numerical difficulty is presented. In this algorithm the equation of continuity rather than the Poisson equation for pressure is solved directly. Pseudospectral formulation of the channel flow problem using Fourier series and Chebyshev polynomials expansions is given for this scheme. An example demonstrating the applicability of the method is given.

Description: The magnitudes of real-gas effects on flat-plate turbulent boundary layer simulations in a cryogenic nitrogen wind tunnel are investigated in order to determine the validity of the method used by Inger (1979) to estimate real-gas effects. Boundary layer solutions for real gases, ideal gases with a specific heat ratio of 1.6 and ideal diatomic gases (specific heat ratio 1.4) were obtained for the worst case conditions of maximum stagnation pressure (9 atm), minimum stagnation temperature (120 K) and Mach number of 1.2. Calculated boundary layer parameters such as friction coefficient and displacement thickness are shown to agree closely for the real gas and the ideal diatomic gas (specific heat ratio 1.4), while the ideal gas solution used by Inger is shown to differ from the real-gas values considerably. Results indicate that real-gas effects on a flat-plate turbulent boundary layer simulation in a cryogenic nitrogen tunnel are insignificant, and suggest the unlikelihood of the large real-gas effects reported by Inger for turbulent boundary layer shock interactions.

Description: Menees (1981) has conducted an evaluation of three different flowfield codes for the Jupiter entry conditions. However, a comparison of the codes has been made difficult by the fact that the three codes use different solution procedures, different computational mesh sizes, and a different convergence criterion. There are also other differences. For an objective evaluation of the different numerical solution methods employed by the codes, it would be desirable to select a simple no-blowing perfect-gas flowfield case for which the turbulent models are well established. The present investigation is concerned with the results of such a study. It is found that the choice of the numerical method is rather problem dependent. The time-marching and the space-marching method provide both comparable results if care is taken in selecting the appropriate mesh size near the body surface.

Description: A set of nonlinear partial differential equations suitable for the description of a class of turbulent three-dimensional flow fields in select geometries is identified. On the basis of the concept of enforcing a penalty constraint to ensure accurate accounting of ordering effects, a finite element numerical solution algorithm is established for the equation set and the theoretical aspects of accuracy, convergence and stability are identified and quantized. Hypermatrix constructions are used to formulate the reduction of the computational aspects of the theory to practice. The robustness of the algorithm, and the computer program embodiment, have been verified for pertinent flow configurations.

Description: A relatively simple one-dimensional thermal model of the Bridgman growth process has been developed which is applicable to the growth of small diameter samples with conductivities similar to those of metallic alloys. The heat flow in a translating rod is analyzed in a way that is applicable to Biot numbers less than unity. The model accommodates an adiabatic zone, different heat transfer coefficients in the hot and cold zones, and changes in sample material properties associated with phase change. The analysis is applied to several simplified cases. The effect of the rod's motion is studied in a three-zone furnace for a rod sufficiently long that end effects can be neglected; end effects are then investigated for a motionless rod. Finally, the addition of a fourth zone, an independently controlled booster heater between the main heater and the adiabatic zone, is evaluated for its ability to increase the gradient in the sample at the melt interface and to control the position of the interface.

Description: Some physical, analytical, and computational aspects of viscous flow are examined with reference to examples of computed flows. The discussion of the physical aspects covers the development of important scales used to reference flow phenomena in laminar and turbulent shear layers; the usefulness of the concepts of circulation and vorticity; and some relatively large-scale organized structures that have recently been identified in transitional and fully developed turbulent flows. Among the analytical aspects discussed are a compact presentation of the compressible Navier-Stokes equations, the Reynolds-averaged form of these equations, and a simplified description of some forms of turbulent models. Finally, results of a simulation of the onset of transition, direct turbulence simulations, and large-eddy simulations are given.

Description: It is pointed out that most practical power generation and propulsion systems involve the burning of different types of fuel sprays, taking into account aircraft propulsion, industrial furnaces, boilers, gas turbines, and diesel engines. There has been a lack of data which can serve as a basis for spray model development and validation. A major aim of the present investigation is to fill this gap. Experimental apparatus and techniques for studying the characteristics of fuel sprays are discussed, taking into account two-dimensional still photography, cinematography, holography, a laser diffraction particle sizer, and a laser anemometer. The considered instruments were used in a number of experiments, taking into account three different types of fuel spray. Attention is given to liquid fuel sprays, high pressure pulsed diesel sprays, and coal-water slurry sprays.

Description: The variable-interval time-averaging (VITA) technique developed by Blackwelder and Kaplan is applied to data obtained from large-eddy simulation of turbulent channel flow in an investigation of the organized structures associated with the bursting phenomenon in the near-wall region. Conditionally averaged velocities, shear stress, pressure, and vorticity are discussed in conjunction with the bursting phenomenon detected by the VITA technique. The conditionally averaged pressure reveals that the ejection process is associated with a localized adverse pressure gradient. In the plane perpendicular to the flow direction, the conditionally averaged vorticity field indicates that a pair of counterrotating streamwise vorticity is being lifted through the ejection process. Previously announced in STAR as N83-17832.

Description: Large-scale coherent structures (CS) in turbulent shear flows are characterized, reviewing recent theoretical and experimental investigations. The use of computers as a research tool and the flow-visualization experimental technique are introduced, CS are defined, the history of their discovery is traced, and their main characteristics are listed. Topics discussed and illustrated include the initial condition of the free shear layer, triple and double decomposition, topological features of CS, detection and eduction of CS, phase alignment via cross correlation, induced versus natural structures, the bursting phenomenon, turbulent spot, streaks, bursting frequency, the axisymmetric mixing layer, vortex pairing in an axisymmetric jet, CS and jet noise, broadband noise amplification via pure-tone excitation, CS interaction in a plane-jet near field, the Taylor hypothesis applied to CS, negative production, and the validity of the Reynolds-number similarity hypothesis. It is found that the coherent Reynolds stress, vorticity, and production are not much greater than the time-averaged values for fully developed flows with significant incoherent turbulence, suggesting that the importance of CS may have been exaggerated in some recent studies.

Description: The process of ablation is calculated for the stagnation region of a flat disk in a radiation-dominated, massive-blowing environment produced in a ballistic range filled with argon. Flow environments are determined by solving the boundary-layer equations while radiative transfer is calculated through a line-by-line spectral computation. The resulting wall heat-transfer rates are coupled with an existing material's response code to determine surface recession and char thickness. The calculation is performed for six 5-cm-diam models made of carbon-phenolic and carbon-carbon composite launched in the Track-G facility at the Arnold Engineering Development Center. Significant surface recessions are predicted to occur for these models due mostly to radiative heating.

Description: A new spectral method for solving the incompressible Navier-Stokes equations in a plane channel and between concentric cylinders is presented. The method uses spectral expansions which inherently satisfy the boundary conditions and the continuity equation and yield banded matrices which are efficiently solved at each time step. In addition, the number of dependent variables is reduced, resulting in a reduction in computer memory requirements. Several test problems have been computed for the channel flow and for flow between concentric cylinders, including Taylor-Couette flow with axisymmetric Taylor vortices and wavy vortices. In all cases, agreement with available experimental and theoretical results is very good.

Description: The solution by multigrid techniques of the steady inviscid compressible equations of gas dynamics, the Euler equations is investigated. Steady two dimensional transonic flow over an airfoil section is studied intensively. Most of the material is applicable to three dimensional flow problems of aerodynamic interest.

Description: Basic concepts associated with the numerical solution of elliptic partial differential equations are introduced, and procedures used to solve the full potential equation for transonic flow fields are discussed. Governing equations, classical relaxation schemes and concepts regarding transonic, full potential equation algorithms are covered. The equation transformation and grid generation procedures; full potential spatial differencing schemes; full potential iteration schemes, emphasizing convergence acceleration; and three dimensional applications are presented.

Description: A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow has been developed. The revision incorporates balancing of massflow rates on each marching step in order to maintain front-to-back continuity during the calculation. Qualitative agreement with analytical predictions and experimental results has been obtained for some flows with well-known solutions.

Description: A method is presented for formulating the boundary conditions in implicit finite-difference form needed for obtaining solutions to the compressible Navier-Stokes equations by the Beam and Warming implicit factored method. The usefulness of the method was demonstrated (a) by establishing the boundary conditions applicable to the analysis of the flow inside an axisymmetric piston-cylinder configuration and (b) by calculating velocities and mass fractions inside the cylinder for different geometries and different operating conditions. Stability, selection of time step and grid sizes, and computer time requirements are discussed in reference to the piston-cylinder problem analyzed.

Description: Transonic viscous-inviscid interaction is considered using the Euler and inverse compressible turbulent boundary-layer equations. Certain improvements in the inverse boundary-layer method are mentioned, along with experiences in using various Runge-Kutta schemes to solve the Euler equations. Numerical conditions imposed on the Euler equations at a surface for viscous-inviscid interaction using the method of equivalent sources are developed, and numerical solutions are presented and compared with experimental data to illustrate essential points. Previously announced in STAR N83-17829

Description: The formal derivation of the three-dimensional parabolic Navier-Stokes equations for subsonic turbulent flow is reviewed. A penalty finite element algorithm is established for numerical solution of the sixteen dependent variable system. Key numerical results are summarized documenting applications in various problem definitions.

Description: Two orthogonal components of velocity and associated Reynolds stresses are determined in a square-sectioned, 90 degree bend of 2.3 radius ratio by utilizing laser-Doppler velocimetry for Reynolds numbers of 790 and 40,000. Results show that boundary layers at the bend inlet of 0.25 and 0.15 of the hydraulic diameter create secondary velocity maxima of 0.6 and 0.4 of the bulk flow velocity, respectively. It is concluded that the boundary layer thickness is important to the flow development, mainly in the first half of the bend, especially when it is reduced to 0.15 of the hydraulic diameter. Smaller secondary velocities are found for turbulent flow in an identical duct with a radius ratio of 7.0 than in the strongly curved bend, although their effect is more important to the streamwise flow development because of the smaller pressure gradients. In addition, the detail and accuracy of the measurements make them suitable for evaluation of numerical techniques and turbulence models.

Description: The model of Warn-Varnas et al. (1978) is used to numerically examine the spin-up flow of a thermally stratified fluid in a cylinder with an insulating side wall, and comparison of the results with the laser-Doppler measurements of Lee (1975) shows excellent agreement. It is shown that flow gradients are created in the interior of the fluid during the meridional circulation spin-up phase, and that the azimuthal flow decayed faster than has been predicted by Wallin (1969). It is established that viscous diffusion in the interior, arising from the interior-flow gradients, is the cause of the discrepancy with Wallin's theory.

Description: A Legendre formulation for a pattern of streamlines adjacent to a surface considered as trajectories with properties consistent with those of a constant vector field is used to develop a mathematical framework for three-dimensional separated flows. Convergence of skin-friction lines onto a particular skin-friction line originating from a particular saddle point is defined as a necessary condition for flow separation. Steady, three-dimensional flow is considered, and singular points occurring in the skin-friction lines are shown to happen where the skin friction or the surface vorticity become zero, and become nodal or saddle points. The separation initiates and continues only globally, as a mixture of an infinite set of friction lines, or locally, with one line. The topography of streamlines in two-dimensional sections of three-dimensional flows is discussed, and examples are provided of a round-nosed body of revolution at varying angles of attack.

Description: This paper describes an experimental program to determine the heat-transfer characteristics of a combustor and heat-exchanger system in a hybrid solar receiver which utilizes a Stirling engine. The system consists of a swirl combustor with a crossflow heat exchanger composed of a single row of 48 closely spaced curved tubes. In the present study, heat-transfer characteristics of the combustor/heat-exchanger system without a Stirling engine have been studied over a range of operating conditions and output levels using water as the working fluid. Nondimensional heat-transfer coefficients based on total heat transfer have been obtained and are compared with available literature data. The results show significantly enhanced heat transfer for the present geometry and test conditions. Also, heat transfer along the length of the tubes is found to vary, the effect depending upon test condition.

Description: A definition for the large-scale coherent structure is presented, and the nature and role of coherent structures in turbulent shear flows are examined. The equations governing the coherent motions and the experimental considerations as well as constraints in the investigations of coherent structures in wall-bounded and free turbulent shear flows are discussed. Results from a few of our recent and on-going studies of coherent structures in excited and unexcited free turbulent shear flows are reviewed. These results show that coherent structures are dominant in transport in the early stages of their formation, but not in the self-preserving regions of turbulent shear flows.

Description: Accurate heat transfer results are provided for the case of nonisothermal objects. A steady, laminar, free convection boundary layer flow over two-dimensional or rotationally symmetrical bodies of nonuniform surface temperature situated in an ambient fluid of undisturbed temperature is considered analytically. The surface heat flux is given in terms of the Nusselt number and wall derivatives of universal functions for Prandtl numbers of 0.72 and 100 are provided. The method is shown to be valid up to a temperature/radius ratio of 130 deg.

Description: Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.

Description: Linear stability theory is employed in the present analysis of flow stability between two vertical, infinite, rigid coaxial cylinders at different temperatures. These calculations have been prompted by, and are found to be in general agreement with, experiments on succinonitrile. A long, vertical cylinder sample of this material was heated so that a vertical melt annulus formed between the coaxial heater and the surrounding crystal/melt interface. Above a critical Grashof number of about 200, a helical crystal/melt interface formed which steadily rotated about the cylinder axis and whose wave speed was several orders of magnitude lower than the base flow velocity.

Description: Asymptotic and numerical techniques in bifurcation theory are applied to the Young-Laplace equation governing meniscus shape in order to analyze the dependence of the shape and stability of rigidly rotating drops held captive between corotating solid faces on multiple parameters. Asymptotic analysis of the evolution of drop shape from the cylindrical as a function of distance between the solid faces, drop volume, rotational Bond number and gravitational Bond number shows that some shape bifurcations from cylinders to wavy, axisymmetric menisci are ruptured by small changes in drop volume or gravity. Computer calculations of axisymmetric drop shapes based on a finite element representation of the interface and numerical algorithms for tracking shape families and singular points are then used to map drop stability for the four-dimensional parameter space. The results of the asymptotic and numerical analyses are shown to agree well within the limited range of parameters where the asymptotic analysis is valid.

Description: Previously cited in issue 07, p. 969, Accession no. A82-20290

Description: In the first part of this investigation, Goldstein (1983) has shown that the amplitude of the spatially growing Tollmien-Schlichting wave generated by a time-harmonic free-stream disturbance is related to the coefficient multiplying the lowest-order asymptotic eigensolution of the unsteady boundary-layer equation. In the present study, a numerical solution of the unsteady boundary-layer equation is used to relate the amplitude of the asymptotic eigensolution, and consequently of the Tollmien-Schlichting wave, to that of the imposed free-stream disturbance for the special case of a uniformly pulsating stream. It is pointed out that the ideas of this study can be extended to other, more complex bodies and free-stream oscillations.

Description: Previously cited in issue 06, p. 859, Accession no. A82-17739

Description: An alternating direction implicit (ADI) method has been applied to a staggered grid for the computation of convection in a highly stratified fluid. Since artificial viscosity is not needed, subtle effects like the onset of convection can be studied. These computations compare well with the 2-D results by Graham (1975) and also agree with standard Boussinesq results when taken to that limit. Good efficiency has been achieved with a time step hundreds of times larger than the stability limit imposed by the explicit treatment of diffusion and the Courant number is not restricted to be below 1. The Navier-Stokes equation contains cross spatial derivatives which are treated explicitly in most ADI schemes. The destabilizing effect of such a practice on a 2-D model system with second-order spatial derivative terms only was analyzed and found to be not excessive.

Description: (Previously cited in issue 06, p. 860, Accession no. A82-17819)

Description: The formation of turbulence around singular points of a flow such as stagnation points, tangential jumps of velocity, are analyzed. It is proved that turbulence is inevitably generated by the rear stagnation point, but cannot be generated by the nose stagnation point of a streamlined body. Special attention is paid to an evolution of turbulence induced by a tangential jump of velocity. A qualitative analysis of a turbulent flow between two rotating concentric cylinders and around a streamlined cylinder is given.

Description: A new method is derived for solving parabolic partial differential equations arising in transient heat conduction or in boundary-layer flows. The method is based on a combination of the modified differential quadrature (MDQ) method with the rational Runge-Kutta time-integration scheme. It is fully explicit, requires no matrix inversion, and is stable for any time-step for the heat equations. Burgers equation and the one- and two-dimensional heat equations are solved to demonstrate the accuracy and efficiency of the proposed algorithm. The present method is found to be very accurate and efficient when results are compared with analytic solutions.

Description: Rotating baroclinic flow for Richardson number lower than about 1 is studied by means of a finite difference Navier-Stokes model assuming no variations except in the vertical plane that completely contains the density gradient vector. The horizontally infinite channel to which attention is given further assumes periodic boundary conditions at the vertical computational boundaries and no-slip conducting horizontal boundaries. Two configurations are considered. Symmetric baroclinic waves developed in the flows in a manner consistent with linear theory, and it is noted that the structures and energetics of the fully developed waves were dependent on the Prandtl number Pr. For Pr greater than 1, the conversion from potential energy to wave kinetic energy was direct, via temperature and vertical motion correlation, while for Pr of less than 1, conversion proceeded from potential energy to average kinetic energy by means of an induced meridional flow, and then to wave kinetic energy.

Description: Linear stability of the one-dimensional flow between infinite vertical coaxial cylinders induced by heating the inner cylinder is considered for various ratios (kappa) of the inner radius to the outer radius, and for Prandtl numbers (P) appropriate to air and water. For air with P = 0.71 the least stable disturbance is nonaxisymmetric for kappa less than 0.44 and is axisymmetric for kappa greater than 0.44, and in either case the instability is due to the action of the shear forces. For P = 3.5, the situation is similar, except that the asymmetric shear mode is superseded by an axisymmetric instability driven by buoyancy forces for kappa = 0.03-0.16. Wave speeds, wavenumbers, and critical Grashof numbers for these cases and for the case of zero Prandtl number are given.

Description: The shock resolution of Harten's (1982) second-order explicit method for one-dimensional hyperbolic conservation laws is investigated for a two-dimensional gas-dynamic problem. The possible extension to a high resolution implicit method for both one- and two-dimensional problems is also investigated. Applications of Harten's method to the quasi-one-dimensional nozzle problem with two nozzle shapes (divergent and convergent-divergent) and the two-dimensional shock-reflection problem resulted in high shock resolution steady-state numerical solutions.

Description: Incompressible viscous flow fields induced by initial vorticity distributions with bounded support or exponential decay in the far field are investigated. A numerical scheme for the solution of the vorticity distribution and the velocity field is presented with special emphasis on the treatment of the boundary data. The efficiency of the scheme is demonstrated. The present method has been applied to the study of the merging and collision of vortex rings.

Description: The theoretical basis for well posed marching of a Parabolic Navier-Stokes (PNS) computational technique for supersonic flow is discussed and examples given to verify the analysis. It is demonstrated that stable computations can be made even with very small steps in the marching direction. The method is applied to cones at large angle of attack in high Reynolds number, supersonic flow. Streamline trajectories generated from the numerical solutions demonstrate the development of vortex structures of the lee side of the cone. Previously announced in STAR as N83-22551

Description: A numerical procedure for the relaxation solution of the full steady Euler equations is described. By embedding the Euler system in a second order surrogate system, central differencing may be used in subsonic regions while retaining matrix forms well suited to iterative solution procedures and convergence acceleration techniques. Hence, this method allows the development of stable, fully conservative differencing schemes for the solution of quite general inviscid flow problems. Results are presented for both subcritical and shocked supercritical internal flows. Comparisons are made with a standard time dependent solution algorithm. Previously announced in STAR as N82-24859

Description: The physical features of steady and unsteady freestream separating turbulent boundary layers that have been determined by pointwise laser anemometer measurements are outlined. It is seen that the large-scale structures control the outer region's backflow behavior. Near the wall, the mean backflow velocity profile for both the steady and unsteady cases is found to scale on the maximum negative mean velocity and its distance from the wall. A description is given of a scanning laser anemometer that produces nearly instantaneous velocity profiles for examing the temporal features of these large-scale structures. Also described is a 'zero-wake' seeder that supplies particles to the outer shear layer and freestream flow with a minimal disturbance.

Description: The extent of convective and radiative heating for a Saturn entry probe is investigated in the absence and presence of ablation mass injection. The flow in the shock layer is assumed to be axisymmetric, viscous and in local thermodynamic equilibrium. The importance of chemical nonequilibrium effects for both the radiative and convective nonblowing surface heating rates is demonstrated for prescribed entry conditions. Results indicate that the nonequilibrium chemistry can significantly influence the rate of radiative heating to the entry probes. With coupled carbon-phenolic ablation injection, the convective heating rates are reduced substantially. Turbulence has little effect on radiative heating but it increases the convective heating considerably.

Description: Previously cited in issue 08, p. 1213, Accession no. A82-22064

Description: The eigenvalue method, which has been used by researchers in structure mechanics, is applied to problems in heat conduction. Its formulation is decribed in terms of an examination of transient heat conduction in a square slab. Taking advantage of the availability of the exact solution, we compare the accuracy and other numerical properties of the eigenvalue method with those of existing numerical schemes. The comparsion shows that, overall, the eigenvalue method appears to be fairly attractive. Furthermore, only a few dominant eigenvalues and their corresponding eigenvectors need to be computed and retained to yield reasonably high accuracy. Greater savings are attained in the computation time for a transient problem with long time duration and a large computational domain.

Description: Ames Research Center has the lead role among NASA centers to conduct research in computational fluid dynamics. The past, the present, and the future prospects in this field are reviewed. Past accomplishments include pioneering computer simulations of fluid dynamics problems that have made computers valuable in complementing wind tunnels for aerodynamic research. The present facilities include the most powerful computers built in the United States. Three examples of viscous flow simulations are presented: an afterbody with an exhaust plume, a blunt fin mounted on a flat plate, and the space shuttle. The future prospects include implementation of the Numerical Aerodynamic Simulation Processing System that will provide the capability for solving the viscous flow field around an aircraft in a matter of minutes.

Description: The influence of high frequency excitations (HFE) on a fluid is investigated. The response to these excitations is decomposed in two parts: 'slow' motion, which practically remains unchanged during the vanishingly small period tau, and 'fast' motion whose value during this period is negligible in terms of displacements, but is essential in terms of the kinetic energy. After such a decomposition the 'slow' and 'fast' motions become nonlinearly coupled by the corresponding governing equations. This coupling leads to an 'effective' potential energy which imparts some 'elastic' properties to the fluid and stabilizes laminar flows.

Description: A solution method for finding the unknown solidification interface in manufacturing slab ingots as a continuous casting is presented, which involves a product solution in the potential plane and the use of conjugate harmonic functions. It is argued that the method may be more direct for some geometries than the Cauchy boundary value method. Moreover, the usefulness of the Cauchy boundary value method is demonstrated through the example of a nonsymmetric horizontal mold where the walls are offset to support the lower ingot boundary.

Description: A method for approximately analyzing the feedback between downstream and upstream edges in incompressible shear flow is described. The shear flow is modeled by a vortex sheet. Equations for resonance eigenvalues are derived. After the reduction of growth rate by finite shear layer thickness is allowed for, agreement is found between calculated resonances and those that have been observed experimentally.

Description: A new numerical technique for simulating three dimensional, unsteady, incompressible pipe flows is presented and its utility and accuracy is shown. Each vector function in the expansion of the velocity field is divergence free and satisfies the boundary conditions for viscous flow. Some of the benefits of the expansion technique are that pressure is eliminated from the dynamics, only two unknowns per mesh point are required, implicit treatment of the viscous terms is provided at no extra computational cost, and no fractional time steps are required. The method uses spectral expansions: Fourier series in the azimuthal and streamwise directions, and Jacobi polynominals in the radial direction. Previously announced in STAR as N82-31644

Description: Developments in three dimensional, time dependent numerical simulation of turbulent flows bounded by a wall are reviewed. Both direct and large eddy simulation techniques are considered within the same computational framework. The computational spatial grid requirements as dictated by the known structure of turbulent boundary layers are presented. The numerical methods currently in use are reviewed and some of the features of these algorithms, including spatial differencing and accuracy, time advancement, and data management are discussed. A selection of the results of the recent calculations of turbulent channel flow, including the effects of system rotation and transpiration on the flow are included. Previously announced in STAR as N82-28577

Description: An implicit finite-difference method is presented for obtaining steady-state solutions to the time-dependent, conservative Euler equations for flows containing shocks. The method uses a two-point central-difference scheme for the flux derivatives with dissipation added at supersonic points via the retarded density concept. Application of the method to 1-dimensional nozzle flow equations for various combinations of subsonic and supersonic boundary conditions show the method to be very efficient. Residuals are typically reduced to machine zero in approximately 35 time steps for 50 mesh points. For 1-dimensional Euler calculations, it is shown that the scheme offers two advantages over the more widely-used three-point schemes. The first is in regard to application of boundary conditions, and the second relates to the fact that the two-point algorithm is well-conditioned for large time steps.

Description: This paper is concerned with small-amplitude, unsteady, vortical and entropic motion imposed on steady potential flows. It is restricted to the case where the spatial scale of the unsteady motion is small compared to that of the mean flow. Under such conditions, the unsteady motion may be influenced by viscosity even if the mean flow is not. An exact high-frequency (small-wavelength) solution is obtained for the small-amplitude viscous motion imposed on a steady potential flow. It generalizes the one obtained by Pearson (1959) for the homogeneous-strain case to the case of quasi-homogeneous strain. This result is used to study the effect of viscosity on rapidly distorted turbulent flows. Specific numerical results are given for a turbulent flow near a two-dimensional stagnation point.

Description: The steady-state equations of inviscid fluid flow, the Euler equations, are a nonlinear nonelliptic system of equations admitting solutions with discontinuities (for example, shocks). The efficient numerical solution of these equations poses a strenuous challenge to multigrid methods. A multigrid code has been developed for the numerical solution of the Euler equations. In this paper some of the factors that had to be taken into account in the design and development of the code are reviewed. These factors include the importance of choosing an appropriate difference scheme, the usefulness of local mode analysis as a design tool, and the crucial question of how to treat the nonlinearity. Sample calculations of transonic flow about airfoils will be presented. No claim is made that the particular algorithm presented is optimal.

Description: Past work on the influence of Mach number on the viscous and inviscid instability of flat-plate boundary layers is reviewed, and new spatial calculations are presented. These calculations support the previous view that viscosity is only stabilizing for both two- and three-dimensional first-mode waves above M1 = 3.0, and for second-mode waves at all Mach numbers. It is concluded that the calculations of Wazzan, Taghavi, and Keltner that show viscous instability at M1 = 6.0 for first-mode 50 deg waves, and at M1 = 3.0 for two-dimensional second-mode waves, are not correct.

Description: Previously cited in issue 05, p. 635, Accession no. A83-16649

Description: A theory is developed for the stagnation point boundary layer with injection under the hypothesis that turbulence is produced at the wall by injection. From the existing experimental heat transfer rate data obtained in wind tunnels, the wall mixing length is deduced to be a product of a time constant and an injection velocity. The theory reproduces the observed increase in heat transfer rates at high injection rates. For graphite and carbon-carbon composite, the time constant is determined to be 0.0002 sec from the existing ablation data taken in an arc-jet tunnel and a balistic range.

Description: Many of the gas turbine combustors in operation use multiple rows of dilution jets, and some have geometries that are different from circular holes. The data base available in literature is generally applicable to a single row of circular holes. Tests were performed with uniform mainstream conditions for several orifice plate configurations. Temperature and pressure measurements were made in the test section at 4 axial and 11 transverse stations. These measurements were made with a 60-element rake probe. Test results for some of these cases are discussed.

Description: Improved methods of predicting airfoil local metal temperatures require advances in the understanding of the physics and methods of analytically predicting the following four aerothermal loads: hot gas flow over airfoils, heat transfer rates on the gas-side of airfoils, cooling air flow inside airfoils, and heat transfer rates on the coolant-side of airfoils. A systematic building block research approach is being pursued to investigate these four areas of concern from both the experimental and analytical sides. Experimental approaches being pursued start with fundamental experiments using simple shapes and flat plates in wind tunnels, progress to more realistic cold and hot cascade tests using airfoils, continue to progress in large low-speed rigs and turbines and warm turbines, and finally, combine all the interactive effects in tests using real engines or real engine type turbine rigs. Analytical approaches being pursued also build from relatively simple steady two dimensional inviscid flow and boundary layer heat transfer codes to more advanced steady two and three dimensional viscous flow and heat transfer codes. These advanced codes provide more physics to model better the interactive effects and the true real-engine environment.

Description: The primary basis for heat transfer analysis of turbine blades is experimental data obtained in linear cascades. These data have been very valuable in identifying the major heat transfer and fluid flow features of a turbine airfoil. The question of major interest is how well all of these data translate to the rotating turbine blade. It is known from the work of Lokay and Trushin that average heat transfer coefficients on the rotor may be as much as 40 percent above the values measured on the same blades nonrotating. Recent work by Dunn and Holt supports the Russian conclusion. What is lacking is a set of data from a rotating system which is of sufficient detail as to make careful local comparisons between static system in which there is sufficient documentation of the flow field to support the computer analyses being developed today. A second major question is the influence, if any, of the first stator row on the heat transfer of the second stator row after the flow has passed through the rotor. An objective of the present program, is to obtain a detailed set of heat transfer coefficients along the midspan of a blade in a rotating turbine.

Description: Improved turbine durability and performance and reduced development cost will all result from impoved methods of predicting turbine metal temperatures. Better metal temperature prediction methods require improvements in the methods of predicting the hot gas flow over the turbine airfoils and the cooling air flow inside the airfoil and in the methods of predicting the heat transfer rates on both the hot gas side and coolant side of the airfoil. The overall HOST Turbine Heat Transfer effort is directed at improving all four of these areas of concern.

Description: The objective of this 36-month experimental and analytical program is to develop a heat transfer and pressure drop database, computational fluid dynamic techniques, and correlations for multipass rotating coolant passages with and without flow turbulators. The experimental effort will be focused on the simulation of configurations and conditions expected in the blades of advanced aircraft high pressure turbines so that the effects of Coriolis and buoyancy forces on the coolant side flow can be rationally included in the design of turbine blades.

Description: The effects of high-intensity, large-scale turbulence on turbulent boundary-layer heat transfer are studied. Flow fields were produced with turbulence intensities up to 40% and length scales up to several times the boundary layer thickness. In addition, three different types of turbulence will be compared to see whether they have the same effect on the boundary layer. The three are: the far field of a free jet, flow downstream of a grid, and flow downstream of a simulated gas turbine combustor. Each turbulence field will be characterized by several measures: intensity (by component), scale, and spectrum. Heat transfer will be measured on a 2.5 m long, 0.5 m wide flat plate using the energy-balance technique. The same plate will be used in each of the four flow fields; a low-turbulence tunnel for baseline data, and the three flow situations mentioned.

Description: The primary basis for heat transfer analysis of turbine airfoils is experimental data obtained in linear cascades. A detailed set of heat transfer coefficients was obtained along the midspan of a stator and a rotor in a rotating turbine stage. The data are to be compared to standard analyses of blade boundary layer heat transfer. A detailed set of heat transfer coefficients was obtained along the midspan of a stator located in the wake of a full upstream turbine stage. Two levels of inlet turbulence (1 and 10 percent) were used. The analytical capability will be examined to improve prediction of the experimental data.

Description: Advanced 3-D inelastic structural/stress analysis methods and solution strategies for more accurate and yet more cost-effective analysis of combustors, turbine blades, and vanes are being developed. The approach is to develop four different theories, one linear and three higher order with increasing complexities including embedded singularities. Progress in each area is reported.

Description: The objectives of this work are: (1) to extend the technique of direct numerical simulations to turbulent, chemically reacting flows, (2) to test the validity of the method by comparing computational results with laboratory data, and (3) to use the simulations to gain a better understanding of the effects of turbulence on chemical reactions. The effects of both the large scale structure and the smaller scale turbulence on the overall reaction rates are addressed. The relationship between infinite reaction rate and finite reaction rate chemistry is compared with some of the results of calculations with existing theories and laboratory data. The direct numerical simulation method involves the numerical solution of the detailed evolution of the complex turbulent velocity and concentration fields. Using very efficient numerical methods (e.g., pseudospectral methods), the fully nonlinear (possibly low pass filtered) equations of motion are solved and no closure assumptions or turbulence models are used. Statistical data are obtained by performing spatial, temporal, and/or ensemble averages over the computed flow fields.

Description: The present paper will compare temperature field measurements from selected cases in these investigations with distributions calculated with an empirical model based on assumed vertical profile similarity and superposition and with a 3-D elliptic code using a standard K-E turbulence model. The results will show the capability (or lack thereof) of the models to predict the effects of the principle flow and geometric variables.

Description: Fuel spray analyses which are a necessary input to the analytical modeling of the complex mixing and combustion processes which occur in advanced combustor systems are discussed. It is anticipated that by controlling fuel air reaction conditions, combustor temperatures can be better controlled, leading to improved combustion system durability. The capability to measure liquid droplet size, velocity, and number density throughout a fuel spray and to utilize this measurement technique in laboratory benchmark experiments was demonstrated. The experiment to characterize fuel sprays is described. The experiments and data are useful for application to and validation of turbulent flow modeling to improve the design systems of future advanced technology engines.

Description: Most fluid flows are turbulent rather than laminar and the reason for this was studied. One of the earliest explanations was that laminar flow is unstable, and the linear instability theory was first developed to explore this possibility. A series of early papers by Rayleigh produced many notable results concerning the instability of inviscid flows, such as the discovery of inflectional instability. Viscosity was commonly thought to act only to stabilize the flow, and flows with convex velocity profiles appeared to be stable. The investigations that led to a viscous theory of boundary layer instability was reported. The earliest application of linear stability theory to transition prediction calculated the amplitude ratio of the most amplified frequency as a function of Reynolds number for a Blasius boundary layer, and found that this quantity had values between five and nine at the observed Ret. The experiment of Schubauer and Skramstad (1947) completely reversed the prevailing option and fully vindicated the Gottingen proponents of the theory. This experiment demonstrated the existence of instability waves in a boundary layer, their connection with transition, and the quantitative description of their behavior by the theory of Tollmien and Schlichting. It is generally accepted that flow parameters such as pressure gradient, suction and heat transfer qualitatively affect transition in the manner predicted by the linear theory, and in particular that a flow predicted to be stable by the theory should remain laminar. The linear theory, in the form of the e9, or N-factor is today in routine use in engineering studies of laminar flow. The stability theory to boundary layers with pressure gradients and suction was applied. The only large body of numerical results for exact boundary layer solutions before the advent of the computer age by calculating the stability characteristics of the Falkner-Skan family of velocity profiles are given. When the digital computer reached a stage of development which permit the direct solution of the primary differential equations, numerical results were obtained from the linear theory during the next 10 years for many different boundary layer flows: three dimensional boundary layers; free convention boundary layers; compressible boundary layers; boundary layers on compliant walls; a recomputation of Falkner-Skan flows; unsteady boundary layers; and heated wall boundary layers.

Description: A 205 mm transfer standard orifice plate meter assembly, consisting of two orifice plates in series separated by a length of pipe containing a flow straightener, was calibrated in two water flow facilities. Results show that the agreement in the characteristics of such a differential pressure transfer standard package is within 0.17% over a 10:1 range from flow rates of approximately 8 to 80 l/sec. When the range over which the comparison was made was limited to that for which the calibration graphs gave straight lines, the agreement is 0.1% in 3 of the 4 calibrations (0.17% in the fourth).

Description: A viscous-inviscid interaction model for predicting jet entrainment effects on axisymmetric, nozzle afterbodies at subsonic speeds is presented. The model is based on a displacement thickness correction to the inviscid jet boundary that accounts for mixing-induced streamline deflections in the inviscid region. The displacement correction is shown to be related to the local mass entrainment rate and, for thin mixing layers, the model is shown to be analogous to displacement models used in conventional boundary-layer interaction theory. A method is presented for computing the entrainment rate by an overlaid mixing layer model that accounts for the nonsimilar behavior and pressure gradients occurring in the near field region. An iterative scheme for coupling the model to analyses for the external inviscid flow, the external boundary layer, and the inviscid jet exhaust is also given. Results are presented that illustrate the qualitative behavior of the entrainment interaction under various flow conditions and that demonstrate the validity of the model by comparisons with experiment.

Description: The capabilities of large eddy simulation in the prediction and analyses of wall-bounded turbulent shear flows are demonstrated. The dynamical equations for large scale field motions are derived. The computational grid network is described and its relation to the observed physical length scales in the flow are discussed. Some aspects of the mechanics and structure of the flow are examined both in the vicinity of the wall and in regions away from the wall. An attempt is made to correlate numerical results with laboratory observations. Other significant observations and conclusions are presented.

Description: Two methods of turbulence computation are discussed in terms of their basic simularities. It is shown that the two methods are interrelated and that each can gain from advances in the other. The degree of success of a pair of increasingly complex Reynolds stress models to broaden their range of applicability is examined through comparison with experimental data for a variety of flow conditions. An example of a large eddy simulation is presented, compared with experimental results, and used to evaluate the models for pressure rate of strain correlation and dissipation in the Reynolds averaged equations.

Description: A computer code for the evaluation and/or optimization of the predicative potential of second order turbulent closure models in simple two dimensional flow configurations is discussed. A procedure for the numerical solution of the steady constant property Navier-Stokes equations are described together with algebraic, one dimensional and two dimensional equations of turbulence closure models. Four turbulence models are compared with several sets of experimental data. The effects of initial conditions and boundary conditions are also described. The effects of purely numerical parameters, such as mesh size, boundary locations, and convergence criteria are presented.

Description: An iterative collocation technique is described for modeling implicit viscosity in three-dimensional incompressible wall bounded shear flow. The viscosity can vary temporally and in the vertical direction. Channel flow is modeled with a Fourier-Legendre approximation and the mean streamwise advection is treated implicitly. Explicit terms are handled with an Adams-Bashforth method to increase the allowable time-step for calculation of the implicit terms. The algorithm is applied to low amplitude unstable waves in a plane Poiseuille flow at an Re of 7500. Comparisons are made between results using the Legendre method and with Chebyshev polynomials. Comparable accuracy is obtained for the perturbation kinetic energy predicted using both discretizations.

Description: The use of superminicomputers for solving a series of increasingly complex thermal analysis problems is investigated. The approach involved (1) installation and verification of the SPAR thermal analyzer software on superminicomputers at Langley Research Center and Goddard Space Flight Center, (2) solution of six increasingly complex thermal problems on this equipment, and (3) comparison of solution (accuracy, CPU time, turnaround time, and cost) with solutions on large mainframe computers.

Description: Thermocapillary stability characteristics of a horizontal liquid layer heated from below rotating about a vertical axis and subjected to a uniform vertical magnetic field are analyzed under a variety of thermal and electromagnetic boundary conditions. Results based on analytical solutions to the pertinent eigenvalue problems are discussed in the light of earlier work on special cases of the more general problem considered here to show in particular the effects of the heat transfer, nonzero curvature and gravity waves at the two-fluid interface. Although the expected stabilizing action of the Coriolis and Lorentz force fields in this configuration are in evidence the optimal choice of an appropriate range for the relevant parameters is shown to be critically dependent on the interfacial effects mentioned above.

Description: Present knowledge of the mechanisms for production and enrichment and film drops by bursting bubbles is summarized, with particular emphasis on the unsolved problems. Sea salt is by far the major constituent cycled through the Earth's atmosphere each year. Bursting bubbles in the oceans appear to be primarily responsible. These salt particles play a role in the formation of maritime clouds, which in turn affect the Earth's radiation budget. Along with the salt are carried various chemical pollutants and potentially pathogenic microorganisms, often in highly enriched form.

Description: A model of the change in shape of a raindrop is presented. Raindrops measured by two orthogonal cameras were classified by shape and orientation to determine the nature of the oscillation. A physical model based on potential energy was then developed to study the amplitude variation of oscillating drops. The model results show that oscillations occur about the equilibrium axis ratio, but the time average axis ratio if significantly more spherical for large amplitudes because of asymmetry in the surface potential energy. A generalization of the model to oscillations produced by turbulence yields average axis ratios that are consistent with the camera measurements. The model results for average axis ratios were applied to rainfall studies with a dual polarized radar.

Description: Results of a wind tunnel experiment in which electrically uncharged water drops of 500 to 3000 microns equivalent radius are freely suspended in the vertical air stream of the UCLA cloud tunnel are presented. During this suspension the drops were exposed to external vertical electric fields of 500 to 8,000 volts/cm. The change in drop shape with drop size and electric field strength was noted and is discussed in the light of theoretical work cited in the literature which unfortunately does not take into account the effects of air flow past the drop. The wind tunnel study is documented by stills from a 16 mm film record that demonstrates the shape of water drops in response to both hydrodynamic and electric forces.

Description: The shape of a gas bubble which rises through a quiescent incompressible, Newtonian fluid at intermediate Reynolds numbers is considered. Exact numerical solutions for the velocity and pressure fields, as well as the bubble shape, are obtained using finite difference techniques and a numerically generated transformation to an orthogonal, boundary-fitted coordinate system. No restriction is placed on the allowable magnitude of deformation.

Description: Holographic studies were performed which examined the fragmentation process during vapor explosion of a water-in-fuel (hexadecane/water) emulsion droplet. Holograms were taken at 700 to 1000 microseconds after the vapor explosion. Photographs of the reconstructed holograms reveal a wide range of fragment droplet sizes created during the explosion process. Fragment droplet diameters range from below 10 microns to over 100 microns. It is estimated that between ten thousand and a million fragment droplets can result from this extremely violent vapor explosion process. This enhanced atomization is thus expected to have a pronounced effect on vaporization processes which are present during combustion of emulsified fuels.

Description: The configuration of liquid hydrogen inside spherical glass shell ICF target was studied both theoretically and experimentally. Because of the zero contact angle between the .D2 liquid and glass substrate and the limited wetting surface that is continuous, the liquid hydrogen completely covers the interior of the glass shell, resulting in the formation of a void at the center. For this reason, the present problem distinguishes itself from that for a sessile drop sitting on a flat surface. A theory was formulated to calculate the liquid hydrogen configuration by including the London-dispersion force between the liquid and the substrate molecules. The net result is an augmented Bashforth-Adams equation appropriate to a spherical substrate, which is considered to be the major contribution of the present work. Preliminary calculations indicate that this equation accurately models the liquid hydrogen behavior inside a spherical microshell.

Description: The NASTRAN thermal analyzer (NTA) which performs large-scale unified thermo-structural analyses with the NASTRAN (NASA structural analysis) computer program is described. The mathematical similitude between these two distinct disciplines of thermal and structure is examined. It serves as the theoretical basis upon which the implementation of the thermal capability in NASTRAN was accomplished. The program structure, the functional flow, the solution algorithms, the organization of an input data deck and the solution capabilities of NTA are summarized. Emphasis is placed on the interface of the unified approach in thermo-structural analyses where stresses, deflections, vibrations and bucklings induced by the effect of temperature change are of concern. Attentions are also directed to the preprocessor and post processors. As a specially designed preprocessor, the VIEW program is capable of generating exchange factors which can be output, at user's option, in formats compatible with that required by NTA. Two post processors that serve specific objectives are included. They are the thermal variance analysis and the graphical displaying capability of temperatures in color or black and white.

Description: Axisymmetric equilibrium shapes of conducting drops and bubbles, (1) pendant or sessile on one face of a circular parallel-plate capacitor or (2) free and surface-charged, are found by solving simultaneously the free boundary problem consisting of the augmented Young-Laplace equation for surface shape and the Laplace equation for electrostatic field, given the surface potential. The problem is nonlinear and the method is a finite element algorithm employing Newton iteration, a modified frontal solver, and triangular as well as quadrilateral tessellations of the domain exterior to the drop in order to facilitate refined analysis of sharply curved drop tips seen in experiments. The stability limit predicted by this computer-aided theoretical analysis agrees well with experiments.

Description: The asymptotic properties for the small Bond number B of the equilibrium capillary interface interior to a circular cylindrical tube vertically dipped in an infinite reservoir of liquid are discussed. (The Bond number B is a dimensionless parameter which is the ratio of gravitational to capillary forces.) The formal expansion in powers of B of the solution to the differential equation describing the equilibrium surface (as can be obtained by standard perturbation methods) is proved to be truly asymptotic -- to all orders and uniformly in the variable and parameter gamma, the contact angle. Sequences of general estimates, in closed form, from above and from below, are also given for the solution and related functions. The M-th term in these sequences are asymptotically exact to order m. An idiosyncrasy of the problem, crucial in obtaining these estimates, is the absolute monotonicity of the structural function of the system in integral form.

Description: On the basis of both a conventional relativistic nuclear fluid dynamic model and a two fluid generalization that takes into account the interpenetration of the target and projectile upon contact, collisions between heavy nuclei moving at relativistic speeds are calculated. This is done by solving the relevant equations of motion numerically in three spatial dimensions by use of particle in cell finite difference computing techniques. The effect of incorporating a density isomer, or quasistable state, in the nuclear equation of state at three times normal nuclear density, and the effect of doubling the nuclear compressibility coefficient are studied. For the reaction 20Ne + 238U at a laboratory bombarding energy per nucleon of 393 MeV, the calculated distributions in energy and angle of outgoing charged particles are compared with recent experimental data both integrated over all impact parameters and for nearly central collisions.