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NASA NTRS1988

Liquid sprays and flow studies in the direct-injection diesel engine under motored conditions

A two dimensional, implicit finite difference method of the control volume variety, a two equation model of turbulence, and a discrete droplet model were used to study the flow field, turbulence levels, fuel penetration, vaporization, and mixing in diesel engine environments. The model was also used to study the effects of engine speed, injection angle, spray cone angle, droplet distribution, and intake swirl angle on the flow field, spray penetration and vaporization, and turbulence in motored two-stroke diesel engines. It is shown that there are optimum conditions for injection, which depend on droplet distribution, swirl, spray cone angle, and injection angle. The optimum conditions result in good spray penetration and vaporization and in good fuel mixing. The calculation presented clearly indicates that internal combustion engine models can be used to assess, at least qualitatively, the effects of injection characteristics and engine operating conditions on the flow field and on the spray penetration and vaporization in diesel engines.

Nguyen, Hung Lee↗

NASA NTRS1988

The solution of the Elrod algorithm for a dynamically loaded journal bearing using multigrid techniques

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed utilizing a multigrid iteration technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

Woods, Claudia M.↗

NASA NTRS1988

Vibrational Power Flow Analysis of Rods and Beams

A new method to model vibrational power flow and predict the resulting energy density levels in uniform rods and beams is investigated. This method models the flow of vibrational power in a manner analogous to the flow of thermal power in a heat conduction problem. The classical displacement solutions for harmonically excited, hysteretically damped rods and beams are used to derive expressions for the vibrational power flow and energy density in the rod and beam. Under certain conditions, the power flow in these two structural elements will be shown to be proportional to the energy density gradient. Using the relationship between power flow and energy density, an energy balance on differential control volumes in the rod and beam leads to a Poisson's equation which models the energy density distribution in the rod and beam. Coupling the energy density and power flow solutions for rods and beams is also discussed. It is shown that the resonant behavior of finite structures complicates the coupling of solutions, especially when the excitations are single frequency inputs. Two coupling formulations are discussed, the first based on the receptance method, and the second on the travelling wave approach used in Statistical Energy Analysis. The receptance method is the more computationally intensive but is capable of analyzing single frequency excitation cases. The traveling wave approach gives a good approximation of the frequency average of energy density and power flow in coupled systems, and thus, is an efficient technique for use with broadband frequency excitation.

Wohlever, James Christopher↗

NASA NTRS1987

Prediction of tip vortex self-induced motion parameters in terms of rotor blade loading

The self-induced motion of curved vortex filaments at the tip of a helicopter rotor blade is investigated analytically. The derivation of a method for inviscid roll-up (IRU) is presented in detail, with attention to the cutoff-distance reformulation of the problem, a control-volume analysis of the self-induction properties of the vortex core, the adaptation of the roll-up method of Betz (1932) to IRU in three dimensions, the treatment of linear and elliptic loading, vortices with turbulent central cores, and the effect of cutoff distance on helicopter free-wake computations. Numerical results showing the significant effect of core properties on the geometry of a rotor wake in hover are presented in graphs and briefly characterized.

Bliss, Donald B.↗

NASA NTRS1988

Universal limiter for transient interpolation modeling of the advective transport equations: The ULTIMATE conservative difference scheme

A fresh approach is taken to the embarrassingly difficult problem of adequately modeling simple pure advection. An explicit conservative control-volume formation makes use of a universal limiter for transient interpolation modeling of the advective transport equations. This ULTIMATE conservative difference scheme is applied to unsteady, one-dimensional scalar pure advection at constant velocity, using three critical test profiles: an isolated sine-squared wave, a discontinuous step, and a semi-ellipse. The goal, of course, is to devise a single robust scheme which achieves sharp monotonic resolution of the step without corrupting the other profiles. The semi-ellipse is particularly challenging because of its combination of sudden and gradual changes in gradient. The ULTIMATE strategy can be applied to explicit conservation schemes of any order of accuracy. Second-order schemes are unsatisfactory, showing steepening and clipping typical of currently popular so-called high resolution shock-capturing of TVD schemes. The ULTIMATE third-order upwind scheme is highly satisfactory for most flows of practical importance. Higher order methods give predictably better step resolution, although even-order schemes generate a (monotonic) waviness in the difficult semi-ellipse simulation. Little is to be gained above ULTIMATE fifth-order upwinding which gives results close to the ultimate for which one might hope.

Leonard, B. P.↗

NASA NTRS1989

Numerical computation of shock wave-turbulent boundary layer interaction in transonic flow over an axisymmetric curved hill

A control-volume based finite difference computation of a turbulent transonic flow over an axisymmetric curved hill is presented. The numerical method is based on the SIMPLE algorithm, and hence the conservation of mass equation is replaced by a pressure correction equation for compressible flows. The turbulence is described by a k-epsilon turbulence model supplemented by a near-wall turbulence model. In the method, the dissipation rate in the region very close to the wall is obtained from an algebraic equation and that for the rest of the flow domain is obtained by solving a partial differential equation for the dissipation rate. The other flow equations are integrated up to the wall. It is shown that the present turbulence model yields the correct location of the compression shock. The other computational results are also in good agreement with experimental data.

Kim, S.-W.↗

NASA NTRS1989

Transient flow thrust prediction for an ejector propulsion concept

A method for predicting transient thrust augmenting ejector characteristics is introduced. The analysis blends classic self-similar turbulent jet descriptions with a mixing region control volume analysis to predict transient effects in a new way. Details of the theoretical foundation, the solution algorithm, and sample calculations are given.

Drummond, Colin K.↗

NASA NTRS1989

Calculation of reattaching shear layers in divergent channel with a multiple-time-scale turbulence model

Numerical calculations of turbulent reattaching shear layers in a divergent channel are presented. The turbulence is described by a multiple-time-scale turbulence model. The turbulent flow equations are solved by a control-volume based finite difference method. The computational results are compared with those obtained using k-epsilon turbulence models and algebraic Reynolds stress turbulence models. It is shown that the multiple-time-scale turbulence model yields significantly improved computational results than the other turbulence models in the region where the turbulence is in a strongly inequilibrium state.

Kim, S.-W.↗

NASA NTRS1989

Numerical investigation of an internal layer in turbulent flow over a curved hill

The development of an internal layer in a turbulent boundary layer flow over a curved hill is investigated numerically. The turbulence field of the boundary layer flow over the curved hill is compared with that of a turbulent flow over a symmetric airfoil (which has the same geometry as the curved hill except that the leading and trailing edge plates were removed) to study the influence of the strongly curved surface on the turbulence field. The turbulent flow equations are solved by a control-volume based finite difference method. The turbulence is described by a multiple-time-scale turbulence model supplemented with a near-wall turbulence model. Computational results for the mean flow field (pressure distributions on the walls, wall shearing stresses and mean velocity profiles), the turbulence structure (Reynolds stress and turbulent kinetic energy profiles), and the integral parameters (displacement and momentum thicknesses) compared favorably with the measured data. Computational results show that the internal layer is a strong turbulence field which is developed beneath the external boundary layer and is located very close to the wall. Development of the internal layer was more obviously observed in the Reynolds stress profiles and in the turbulent kinetic energy profiles than in the mean velocity profiles. In this regard, the internal layers is significantly different from wall-bounded simple shear layers in which the mean velocity profile characterizes the boundary layer most distinguishably. Development of such an internal layer, characterized by an intense turbulence field, is attributed to the enormous mean flow strain rate caused by the streamline curvature and the strong pressure gradient. In the turbulent flow over the curved hill, the internal layer begin to form near the forward corner of the hill, merges with the external boundary layer, and develops into a new fully turbulent boundary layer as the fluid flows in the downstream direction. For the flow over the symmetric airfoil, the boundary layer began to form from almost the same location as that of the curved hill, grew in its strength, and formed a fully turbulent boundary layer from mid-part of the airfoil and in the downstream region. Computational results also show that the detailed turbulence structure in the region very close to the wall of the curved hill is almost the same as that of the airfoil in most of the curved regions except near the leading edge. Thus the internal layer of the curved hill and the boundary layer of the airfoil were also almost the same. Development of the wall shearing stress and separation of the boundary layer at the rear end of the curved hill mostly depends on the internal layer and is only slightly influenced by the external boundary layer flow.

Kim, S-W.↗

NASA NTRS1989

Experimental results for labyrinth gas seals with honeycomb stators - Comparisons to smooth-stator seals and theoretical predictions

Experimental measurements are presented for the rotordynamic stiffness and damping coefficients of a teeth-on-rotor labyrinth seal with a honeycomb stator. Inlet circumferential velocity, inlet pressure, rotor speed, and seal clearance are primary variables. Results are compared to data for teeth-on-rotor labyrinth seals with smooth stators and to analytical predictions from a two-control-volume compressible flow model. The experimental results show that the honeycomb-stator configuration is more stable than the smooth-stator configuration at low rator speeds. At high rotor speeds, the stator surface does not affect stability. The theoretical model predicts the cross-coupled stiffness of the honeycomb-stator seal correctly within 25 percent of measured values. The model provides accurate predictions of direct damping for large clearance seals; however, the model predictions and test results diverge with increasing running speed. Overall, the model does not perform as well for low clearance seals as for high clearance seals.

Hawkins, Larry↗

NASA NTRS1989

The design and application of upwind schemes on unstructured meshes

Solution and mesh generation algorithms for solving the Euler equations on unstructured meshes consisting of triangle and quadrilateral control volumes are presented. Cell-centered and mesh-vertex upwind finite-volume schemes are developed which utilize multi-dimensional monotone linear reconstruction procedures. These algorithms differ from existing algorithms (even on structured meshes). Numerical results in two dimensions are presented.

Barth, Timothy J.↗

NASA NTRS1989

The solution of the Elrod algorithm for a dynamically loaded journal bearing using multigrid techniques

Woods, C. M.↗

NASA NTRS1989

Transient flow thrust prediction for an ejector propulsion concept

Drummond, C.↗

NASA NTRS1989

A numerical analysis of Stefan problems for generalized multi-dimensional phase-change structures using the enthalpy transforming model

An enthalpy transforming scheme is proposed to convert the energy equation into a nonlinear equation with the enthalpy, E, being the single dependent variable. The existing control-volume finite-difference approach is modified so it can be applied to the numerical performance of Stefan problems. The model is tested by applying it to a three-dimensional freezing problem. The numerical results are in agreement with those existing in the literature. The model and its algorithm are further applied to a three-dimensional moving heat source problem showing that the methodology is capable of handling complicated phase-change problems with fixed grids.

Cao, Yiding↗

NASA NTRS1989

A parametric heat transfer study for cryogenic ball bearings in SSME HPOTP

A numerical modeling is to examine the effects of coolant convective heat transfer coefficient and frictional heating on the local temperature characteristics of a ball element in Space Shuttle Main Engine (SSME) High Pressure Oxidizer Turbopump (HPOTP) bearing. The present modeling uses a control-volume based, finite-difference method to solve the non-dimensionalized heat conduction equation in spherical coordinate system. The dimensionless temperature is found as a function of Biot number, heat flux ratio between the two race contacts, and location in the ball. The current results show that, for a given cooling capability, the ball temperature generally increases almost linearly with the heat input from the race-contacts. This increase is always very high at one of the two contacts. An increase in heat transfer coefficient generally reduces the ball temperature and alleviates the temperature gradient, except for the regions very close to the race contacts. For a 10-fold increase of heat transfer coefficient, temperature decrease is 35 percent for the average over entire ball, and 10 percent at the inner-race contact. The corresponding change of temperature gradient displays opposing trends between the regions immediately adjacent to the contacts and the remaining portion of the ball. The average temperature gradient in the vicinity of both contacts increases approximately 70 to 100 percent. A higher temperature gradient produces excessive thermal stress locally which may be detrimental to the material integrity. This, however, is the only unfavorable issue for an increase of heat transfer coefficient.

Chyu, Mingking K.↗

NASA NTRS1989

Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville, Apr. 3-7, 1989

Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.

Chung, T. J.↗

NASA NTRS1990

Calculation of reattaching shear layers in divergent channel with a multiple-time-scale turbulence model

Kim, S.-W.↗

NASA NTRS1990

Thermal buoyancy and Marangoni convection in a two fluid layered system - A numerical study

Thermal buoyancy and surface tension driven convection is numerically investigated in a system with two, immiscible fluids. The geometry investigated, has an open cavity configuration with the lighter fluid situated on top of the heavier fluid, forming a stable layered system. The upper fluid meniscus and the interface are assumed to be flat and undeformable in the calculations. The governing equations and boundary/interface conditions are solved by a control volume based finite difference scheme for two pairs of immiscible fluids; the water-hexadecane system and a so called generic system. The steady state calculations show, that dramatically different flows are predicted when the interfacial tension effects are included or excluded from the system model. These differences are particularly appreciable in surface tension dominated flows, that are typical of microgravity situations. Complex flow patterns, with induced secondary flows are noticed in both the fluids. In general, the overall system heat transfer is found to increase with increases in the thermal buoyancy and surface tension effects, but the behavior of the system flow and thermal fields is not easy to characterize, when different combinations of these forces are considered.

Ramachandran, N.↗