Search NASA⌕ Search

SEARCH · Search NASA

Results for “Conservative variables”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5

Vibration Reduction of Helicopter Blade Using Variable Dampers: A Feasibility Study

In the report, the investigation of controlling helicopter-blade lead-lag vibration is described. Current practice of adding passive damping may be improved to handle large dynamic range of the blade with several peaks of vibration resonance. To minimize extra-large damping forces that may damage the control system of blade, passive dampers should have relatively small damping coefficients, which in turn limit the effectiveness. By providing variable damping, a much larger damping coefficient to suppress the vibration can be realized. If the damping force reaches the maximum allowed threshold, the damper will be automatically switched into the mode with smaller damping coefficient to maintain near-constant damping force. Furthermore, the proposed control system will also have a fail-safe feature to guarantee the basic performation of a typical passive damper. The proposed control strategy to avoid resonant regions in the frequency domain is to generate variable damping force in combination with the supporting stiffness to manipulate the restoring force and conservative energy of the controlled blade system. Two control algorithms are developed and verified by a prototype variable damper, a digital controller and corresponding algorithms. Primary experiments show good potentials for the proposed variable damper: about 66% and 82% reductions in displacement at 1/3 length and the root of the blade respectively.

Lee, George C.↗

A rapid implicit-explicit solution to the two-dimensional time dependent incompressible Navier-Stokes equations

A second-order time-accurate and spatially factored algorithm was used in a finite difference scheme for the numerical solution of the time-dependent, incompressible, two dimensional Navier-Stokes equations in conservation-law form using vorticity and stream function variables. The systems of equations are solved at each time step by an iterative technique. Numerical results were obtained for a circular cylinder at a Reynolds number of 15, and an NACA 0012 airfoil at zero angle of attack at Reynolds numbers of 10 to the third and 10 to the fourth powers. The results are in agreement with another numerical technique, and the computing time required to obtain the steady state solution at the Reynolds number of 10 to the 4th power was 49.7 sec on CDC 7600 computer using a 65 x 84 computational grind.

Davis, J. E.↗

The evolution of AAOE observed constituents with the polar vortex

One of the difficulties in determining constituent trends from the ER-2 flight data is the large amount of day to day variability generated by the motion of the polar vortex. To reduce this variability, the observations have been transformed into the conservative (Lagrangian) reference frames consisting of the coordinate pairs, potential temperature (PT) and potential vorticity (PV), or PT and N2O. The requirement of only two independent coordinates rests on the assumption that constituent distributions and their chemical processes are nearly zonal in that coordinate system. Flight data is used everywhere for these transformation except for potential vorticity. Potential vorticity is determined from level flight segments, and NMC PV values during flight dives and takeoffs are combined with flight data in a smooth fashion.

Schoeberl, Mark R.↗

A guide to the use of theoretical models of the solar nebula for the interpretation of the meteoritic record

Attempts to derive a theoretical framework for the interpretation of the meteoritic record have been frustrated by our incomplete understanding of the fundamental processes that controlled the evolution of the primitive solar nebula. Nevertheless, it is possible to develop qualitative models of the nebula that illuminate its dynamic character, as well as the roles of some key parameters. These models draw on the growing body of observational data on the properties of disks around young, solar-type stars, and are constructed by applying the results of known solutions of protostellar collapse problems; making simple assumptions about the radial variations of nebular variables; and imposing the integral constraints demanded by conservation of mass, angular momentum, and energy. The models so constructed are heuristic, rather than predictive; they are intended to help us think about the nebula in realistic ways, but they cannot provide a definitive description of conditions in the nebula.

Cassen, Pat↗

Volume 2: Explicit, multistage upwind schemes for Euler and Navier-Stokes equations

The objective of this study was to develop a high-resolution-explicit-multi-block numerical algorithm, suitable for efficient computation of the three-dimensional, time-dependent Euler and Navier-Stokes equations. The resulting algorithm has employed a finite volume approach, using monotonic upstream schemes for conservation laws (MUSCL)-type differencing to obtain state variables at cell interface. Variable interpolations were written in the k-scheme formulation. Inviscid fluxes were calculated via Roe's flux-difference splitting, and van Leer's flux-vector splitting techniques, which are considered state of the art. The viscous terms were discretized using a second-order, central-difference operator. Two classes of explicit time integration has been investigated for solving the compressible inviscid/viscous flow problems--two-state predictor-corrector schemes, and multistage time-stepping schemes. The coefficients of the multistage time-stepping schemes have been modified successfully to achieve better performance with upwind differencing. A technique was developed to optimize the coefficients for good high-frequency damping at relatively high CFL numbers. Local time-stepping, implicit residual smoothing, and multigrid procedure were added to the explicit time stepping scheme to accelerate convergence to steady-state. The developed algorithm was implemented successfully in a multi-block code, which provides complete topological and geometric flexibility. The only requirement is C degree continuity of the grid across the block interface. The algorithm has been validated on a diverse set of three-dimensional test cases of increasing complexity. The cases studied were: (1) supersonic corner flow; (2) supersonic plume flow; (3) laminar and turbulent flow over a flat plate; (4) transonic flow over an ONERA M6 wing; and (5) unsteady flow of a compressible jet impinging on a ground plane (with and without cross flow). The emphasis of the test cases was validation of code, and assessment of performance, as well as demonstration of flexibility.

Elmiligui, Alaa↗

Heat Transfer from Radiatively Heated Material in a Low Reynolds Number Microgravity Environment

A mathematical model of the transient three-dimensional heat transfer between a slowly moving ambient gas stream and a thermally thick or thin flat surface heated by external radiation in a microgravity environment is presented. The problem is motivated in part by fire safety issues in spacecraft. The gas phase is represented by variable property convection-diffusion energy and mass conservation equations valid at low Reynolds numbers. The absence of gravity and low Reynolds number together permit the flow to be represented by a self-consistent velocity potential determined by the ambient velocity and the thermal expansion in the gas. The solid exchanges energy with the gas by conduction/convection and with the surroundings by surface absorption and re-emission of radiation. Heat conduction in the solid is assumed to be one dimensional at each point on the surface as a consequence of the limited times (of order of 10 seconds) of interest in these simulations. Despite the apparent simplicity of the model, the results show a complex thermally induced flow near the heated surface. The thermal exchange between the gas and solid produces an outward sourcelike flow upstream of the center of the irradiated area and a sinklike flow downstream. The responses of the temperature fields and the associated flows to changes in the intensity of the external radiation and the ambient velocity are discussed.

Yamashita, H.↗

Three Dimensional Flow and Pressure Patterns in a Single Pocket of a Hydrostatic Journal Bearing

The flow in a hydrostatic pocket is described by a mathematical model that uses the three dimensional Navier-Stokes equations written in terms of the primary variables, u, v, w, and p. Using a conservative formulation, a finite volume multi-block method is applied through a collocated, body fitted grid. The flow is simulated in a shallow pocket with a depth/length ratio of 0.02. The flow structures obtained and described by the authors in their previous two dimensional models are made visible in their three dimensional aspect for the Couette flow. It has been found that the flow regimes formed central and secondary vortical cells with three dimensional corkscrew-like structures that lead the fluid on an outward bound path in the axial direction of the pocket. The position of the central vortical cell center is at the exit region of the capillary restrictor feedline. It has also been determined that a fluid turn around zone occupies all the upstream space between the floor of the pocket and the runner, thus preventing any flow exit through the upstream port. The corresponding pressure distribution under the shaft presented as well. It was clearly established that for the Couette dominated case the pressure varies significantly in the pocket in the circumferential direction, while its variation is less pronounced axially.

Braun, M. Jack↗

The Dynamics of Miscible Interfaces: Simulations

The goal of this experimental/computational investigation (joint with Prof Maxworthy at USC) has been to study the dynamics of miscible interfaces, both from a scientific and a practical point of view, and to prepare a related experiment to be flown on the International Space Station. In order to address these effects, we have focused experimental and computational investigations on miscible displacements in cylindrical capillary tubes, as well as in Hele-Shaw cells. Regarding the flow in a capillary tube, the question was addressed as to whether Korteweg stresses and/or divergence effects can potentially account for discrepancies observed between conventional Stokes flow simulations and experiments for miscible flows in capillary tubes. An estimate of the vorticity and streamfunction fields induced by the Kortewegs stresses was derived, which shows these stresses to result in the formation of a vortex ring structure near the tip of the concentration front. Through this mechanism the propagation velocity of the concentration front is reduced, in agreement with the experimental observations. Divergence effects, on the other hand, were seen to be very small, and they have a negligible influence on the tip velocity. As a result, it can be concluded that they are not responsible for the discrepancies between experiments and conventional Stokes simulations. A further part of our investigation focussed on the development of high-accuracy three-dimensional spectral element simulation techniques for miscible flows in capillary tubes, including the effects of variable density and viscosity. Towards this end, the conservation equations are treated in cylindrical coordinates.

Meiburg, Eckart↗

A Vertically Lagrangian Finite-Volume Dynamical Core for Global Models

A finite-volume dynamical core with a terrain-following Lagrangian control-volume discretization is described. The vertically Lagrangian discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water dynamical system. The 2D horizontal-to-Lagrangian-surface transport and dynamical processes are then discretized using the genuinely conservative flux-form semi-Lagrangian algorithm. Time marching is split- explicit, with large-time-step for scalar transport, and small fractional time step for the Lagrangian dynamics, which permits the accurate propagation of fast waves. A mass, momentum, and total energy conserving algorithm is developed for mapping the state variables periodically from the floating Lagrangian control-volume to an Eulerian terrain-following coordinate for dealing with physical parameterizations and to prevent severe distortion of the Lagrangian surfaces. Deterministic baroclinic wave growth tests and long-term integrations using the Held-Suarez forcing are presented. Impact of the monotonicity constraint is discussed.

Lin, Shian-Jiann↗

Investigating Response from Attached and Separated Flow Excitations on a Real Launch Vehicle using SEA

Statistical Energy Analysis (SEA) response has been fairly well anchored to test observations for Diffuse Acoustic Field (DAF) loading by others. Meanwhile, not many examples can be found in the literature anchoring the SEA vehicle panel response results to Turbulent Boundary Layer (TBL) fluctuating pressure excitations. This deficiency is especially true for supersonic trajectories such as those required by this nation s launch vehicles. Response and excitation data from vehicle flight measurements gathered during the development flight era of the Space Shuttle have been used in a trial to assess the sensitivity of response analysis to certain known and unknown parameters of the flight. This assessment compares vibration response predictions for TBL excitations produced by the SEA tool to flight measurements. A secondary, but perhaps more important objective, is to provide more clarity concerning the accuracy and conservatism that can be expected from response estimates to TBL-excited vehicle models in SEA. What range of parameters must be included in such an analysis in order to land on the conservative side in response predictions? What is the variability produced in the results with changes in these parameters? The TBL fluid structure loading model used for this study is provided from the SEA module of the commercial code VA One.

Harrison, Phil↗

Compact Augmented Spark Igniters for Liquid Rocket Engines

The objective of this dissertation is to characterize augmented spark impinging (torch) igniters. Torch igniters inject propellants into a small prechamber where a spark igniter imparts the activation energy to initiate combustion. The flame stabilizes within the prechamber and exits into the main combustion chamber where it ignites the main flow directly or by mixing with a coaxial flow to create a secondary flame. The underlying phenomena that promote reliable ignition are multifaceted and required a broad scope of investigations. Initial efforts focused on spark discharges across an annular geometry. Gaseous propellent projects the electrical arc toward the prechamber, where the arc and the thermal energy is imparted to the surrounding fluid then meets with a combustible mixture. Discharges are parametrically examined against pressure, spark-gap size, and exciter types to emulate transient engine startup. The energy imparted to the flow, approximate velocity, and distance traveled by the exhaust plume are determined. Spark quenching (no energy deposition) and its effects on perceived versus actual measurements are shown. Results outline the prechamber target zone where a combustible mixture is necessary for ignition. Next, three-dimensional, time-accurate, and nonreacting computational fluid dynamics simulations assess effects of geometric and mass flow differences on the size, location, and composition of a combustible mixture. Fluid dynamic phenomena are elucidated. Correlations between nondimensional variables are found. Results are coupled with a conservation-law analysis to produce novel objective functions. Lastly, a full-scale, modular torch igniter is tested. Injector sizes, mixture ratios, and injector momentum ratios are systematically varied to map ignition probability and ignition delay. Results show the importance of local mixture ratios, provide injector momentum ratios guidelines, and demonstrate reliable ignition of core mixture ratios typically outside flammability limits. The deliverable of this project is not a torch igniter or derivative thereof. Instead, this dissertation produces novel objective-functions for igniter design. These equations are functions of variables that may be constrained by engine-level requirements, physics, and experimental results from this work. They provide a foundation for future igniter design and will minimize iterative processes from the design cycle for next-generation ignition hardware.

Torch Igniter↗

Applications of film thickness equations

A number of applications of elastohydrodynamic film thickness expressions were considered. The motion of a steel ball over steel surfaces presenting varying degrees of conformity was examined. The equation for minimum film thickness in elliptical conjunctions under elastohydrodynamic conditions was applied to roller and ball bearings. An involute gear was also introduced, it was again found that the elliptical conjunction expression yielded a conservative estimate of the minimum film thickness. Continuously variable-speed drives like the Perbury gear, which present truly elliptical elastohydrodynamic conjunctions, are favored increasingly in mobile and static machinery. A representative elastohydrodynamic condition for this class of machinery is considered for power transmission equipment. The possibility of elastohydrodynamic films of water or oil forming between locomotive wheels and rails is examined. The important subject of traction on the railways is attracting considerable attention in various countries at the present time. The final example of a synovial joint introduced the equation developed for isoviscous-elastic regimes of lubrication.

Hamrock, B. J.↗

Fast and optimal solution to the Rankine-Hugoniot problem

A new, definitive, reliable and fast iterative method is described for determining the geometrical properties of a shock (i.e., theta sub Bn, yields N, V sub s and M sub A), the conservation constants and the self-consistent asymptotic magnetofluid variables, that uses the three dimensional magnetic field and plasma observations. The method is well conditioned and reliable at all theta sub Bn angles regardless of the shock strength or geometry. Explicit proof of uniqueness of the shock geometry solution by either analytical or graphical methods is given. The method is applied to synthetic and real shocks, including a bow shock event and the results are then compared with those determined by preaveraging methods and other iterative schemes. A complete analysis of the confidence region and error bounds of the solution is also presented.

Vinas, A. F.↗

Numerical techniques for large cosmological N-body simulations

Techniques for carrying out large N-body simulations of the gravitational evolution of clustering in the fundamental cube of an infinite periodic universe are described and compared. The accuracy of the forces derived from several commonly used particle mesh schemes is examined, showing how submesh resolution can be achieved by including short-range forces between particles by direct summation techniques. The time integration of the equations of motion is discussed, and the accuracy of the codes for various choices of 'time' variable and time step is tested by considering energy conservation as well as by direct analysis of particle trajectories. Methods for generating initial particle positions and velocities corresponding to a growing mode representation of a specified power spectrum of linear density fluctuations are described. The effects of force resolution are studied and different simulation schemes are compared. An algorithm is implemented for generating initial conditions by varying the number of particles, the initial amplitude of density fluctuations, and the initial peculiar velocity field.

Efstathiou, G.↗

Fast and optimal solution to the 'Rankine-Hugoniot problem'

A new, definitive, reliable and fast iterative method is described for determining the geometrical properties of a shock (i.e., theta sub Bn, yields N, V sub s and M sub A), the conservation constants and the self-consistent asymptotic magnetofluid variables, that uses the three dimensional magnetic field and plasma observations. The method is well conditioned and reliable at all theta sub Bn angles regardless of the shock strength or geometry. Explicit proof of uniqueness of the shock geometry solution by either analytical or graphical methods is given. The method is applied to synthetic and real shocks, including a bow shock event and the results are then compared with those determined by preaveraging methods and other iterative schemes. A complete analysis of the confidence region and error bounds of the solution is also presented.

Vinas, A. F.↗

A time-accurate algorithm for chemical non-equilibrium viscous flows at all speeds

A time-accurate, coupled solution procedure is described for the chemical nonequilibrium Navier-Stokes equations over a wide range of Mach numbers. This method employs the strong conservation form of the governing equations, but uses primitive variables as unknowns. Real gas properties and equilibrium chemistry are considered. Numerical tests include steady convergent-divergent nozzle flows with air dissociation/recombination chemistry, dump combustor flows with n-pentane-air chemistry, nonreacting flow in a model double annular combustor, and nonreacting unsteady driven cavity flows. Numerical results for both the steady and unsteady flows demonstrate the efficiency and robustness of the present algorithm for Mach numbers ranging from the incompressible limit to supersonic speeds.

Shuen, J.-S.↗

A coupled implicit method for chemical non-equilibrium flows at all speeds

The present time-accurate coupled-solution procedure addresses the chemical nonequilibrium Navier-Stokes equations over a wide Mach-number range uses, in conjunction with the strong conservation form of the governing equations, five unknown primitive variables. The numerical tests undertaken address steady convergent-divergent nozzle flows with air dissociation/recombination, dump combustor flows with n-pentane/air chemistry, and unsteady nonreacting cavity flows.

Shuen, Jian-Shun↗

Combustion Of Moving Droplets And Of Droplets Suspended Within A Convective Environment: Transient Numerical Results

The problem considered is that of a single-component liquid fuel (n-heptane) droplet undergoing evaporation and combustion in a hot, convective, low pressure, zero-gravity environment of infinite expanse. For a moving droplet, the relative velocity (U(sub infinity)) between the droplet and freestream is subject to change due to the influence of the drag force on the droplet. For a suspended droplet, the relative velocity is kept constant. The governing equations for the gas-phase and the liquid-phase consist of the unsteady, axisymmetric equations of mass, momentum, species (gas-phase only) and energy conservation. Interfacial conservation equations are employed to couple the two phases. Variable properties are used in the gas- and liquid-phase. Multicomponent diffusion in the gas-phase is accounted for by solving the Stefan-Maxwell equations for the species diffusion velocities. A one-step overall reaction is used to model the combustion. The governing equations are discretized using the finite volume and SIMPLEC methods. A colocated grid is adopted. Hyperbolic tangent stretching functions are used to concentrate grid points near the fore and aft lines of symmetry and at the droplet surface in both the gas- and liquid-phase. The discretization equations are solved using the ADI method with the TDMA used on each line of the two alternating directions. Iterations are performed within each time-step until convergence is achieved. The grid spacing, size of the computational domain and time-step were tested to ensure that all solutions are independent of these parameters. A detailed discussion of the numerical model is given.

Gogos, George↗