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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.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1955

A method of quadrature for calculation of the laminar and turbulent boundary layer in case of plane and rotationally symmetrical flow

For calculation of the characteristic parameters of the boundary layer (momentum-loss thickness and form parameter for the velocity profile), two quadrature formulas are given which are valid for the laminar as well as for the turbulent state of flow. These formulas cover both the two-dimensional and the rotationally symmetrical case. The calculation of the momentum-loss thickness is carried out by a simple integration of the energy theorem. The equation for the form parameter is obtained by coupling of the momentum theorem with the energy theorem. Knowledge of the derivatives of the velocity distribution and of the radius of the body along the length x is not necessary.

FLOW, TURBULENT↗
NASA NTRS1992

Energetic particle transport in relativistic flows

A discussion is given of pitch angle dependent and diffusive transport equations for cosmic rays applicable for both special relativistic and general relativistic flows, derived from the relativistic Boltzmann equation. As an example of particle transport in a curved spacetime we give a pitch angle dependent transport equation appropriate for radial accretion onto a Schwarzschild black hole. The roles of fluid shear, acceleration and compression on the energy changes of particles in the diffusive transport equations are emphasized. Also discussed are special flows (e.g. rigidly rotating flows) associated with a Killing vector for which a constant of the motion of the particles can be identified, and for which simplified transport equations can be constructed.

Webb, G. M.↗
NASA NTRS1994

Green's formula and variational principles for cosmic-ray transport with application to rotating and shearing flows

Green's theorem and Green's formula for the diffusive cosmic-ray transport equation in relativistic flows are derived. Green's formula gives the solution of the transport equation in terms of the Green's function of the adjoint transport equation, and in terms of distributed sources throughout the region R of interest, plus terms involving the particle intensity and streaming on the boundary. The adjoint transport equation describes the time-reversed particle transport. An Euler-Lagrange variational principle is then obtained for both the mean scattering frame distribution function f, and its adjoint f(dagger). Variations of the variational functional with respect to f(dagger) yield the transport equation, whereas variations of f yield the adjoint transport equation. The variational principle, when combined with Noether's theorem, yields the conservation law associated with Green's theorem. An investigation of the transport equation for steady, azimuthal, rotating flows suggests the introduction of a new independent variable H to replace the comoving frame momentum variable p'. For the case of rigid rotating flows, H is conserved and is shown to be analogous to the Hamiltonian for a bead on a rigidly rotating wire. The variable H corresponds to a balance between the centrifugal force and the particle inertia in the rotating frame. The physical interpretation of H includes a discussion of nonrelativistic and special relativistic rotating flows as well as the cases of aziuthal, differentially rotating flows about Schwarzs-child and Kerr black holes. Green's formula is then applied to the problem of the acceleration of ultra-high-energy cosmic rays by galactic rotation. The model for galactic rotation assumes an angular velocity law Omega = Omega(sub 0)(omega(sub 0)/omega), where omega denotes radial distance from the axis of rotation. Green's functions for the galactic rotation problem are used to investigate the spectrum of accelerated particles arising from monoenergetic and truncated power-law sources. We conclude that it is possible to accelerate particles beyond the knee by galactic rotation, but not in sufficient number to adequately explain the observed spectrum.

Webb, G. M.↗
NASA NTRS1990

Numerical simulation of transition in a rotating disk flow

An investigation of the laminar-turbulence transition process in a three-dimensional boundary layer on a rotating disk is initiated. Preliminary results from a direct numerical simulation using spectral collocation method are presented. The simulation results in the linear regime is tested against linear stability theory. Saturation of the primary disturbance energy suggests the importance of modal interaction in initiating transition.

Balachandar, S.↗
NASA NTRS1971

Some characteristics of turbulent boundary layers in rapidly accelerated flows

An analysis of time-mean-turbulent boundary layer velocity profiles measured in a rapidly accelerating flow suggests that the outer region of the velocity profiles consists of essentially inviscid, rotational flow. The extent of this inviscid outer region was observed in some cases to exceed 90 percent of what is ordinarily thought of as the turbulent boundary layer thickness. On the other hand, the inner frictional region of these velocity profiles appears to have turbulent characteristics similar to those of more conventional turbulent boundary layers. Hence, the outer edge boundary condition for this inner region is more properly the external rotational flow region than the free stream.

Brinich, P. F.↗
NASA NTRS1987

A three-dimensional dual potential procedure with applications to wind tunnel inlets and interacting boundary layers

A dual potential decomposition of the velocity field into a scalar and a vector potential function is extended to three dimensions and used in the finite-difference simulation of steady three-dimensional inviscid rotational flows and viscous flow. The finite-difference procedure was used to simulate the flow through the 80 by 120 ft wind tunnel at NASA Ames Research Center. Rotational flow produced by the stagnation pressure drop across vanes and screens which are located at the entrance of the inlet is modeled using actuator disk theory. Results are presented for two different inlet vane and screen configurations. The numerical predictions are in good agreement with experimental data. The dual potential procedure was also applied to calculate the viscous flow along two and three dimensional troughs. Viscous effects are simulated by injecting vorticity which is computed from a boundary layer algorithm. For attached flow over a three dimensional trough, the present calculations are in good agreement with other numerical predictions. For separated flow, it is shown from a two dimensional analysis that the boundary layer approximation provides an accurate measure of the vorticity in regions close to the wall; whereas further away from the wall, caution has to be exercised in using the boundary-layer equations to supply vorticity to the dual potential formulation.

Rao, K. V.↗
NASA NTRS1977

Computation of unsteady transonic flows through rotating and stationary cascades. 1: Method of analysis

A numerical method of solution of the inviscid, compressible, two-dimensional unsteady flow on a blade-to-blade stream surface through a stage (rotor and stator) or a single blade row of an axial flow compressor or fan is described. A cyclic procedure has been developed for representation of adjacent blade-to-blade passages which asymptotically achieves the correct phase between all passages of a stage. A shock-capturing finite difference method is employed in the interior of the passage, and a method of characteristics technique is used at the boundaries. The blade slipstreams form two of the passage boundaries and are treated as moving contact surfaces capable of supporting jumps in entropy and tangential velocity. The Kutta condition is imposed by requiring the slipstreams to originate at the trailing edges, which are assumed to be sharp. Results are presented for several transonic fan rotors and compared with available experimental data, consisting of holographic observations of shock structure and pressure contour maps. A subcritical stator solution is also compared with results from a relaxation method. Finally, a periodic solution for a stage consisting of 44 rotor blades and 46 stator blades is discussed.

Erdos, J. I.↗
NASA NTRS1975

Form of the turbulence dissipation equation as applied to curved and rotating turbulent flows

An exact turbulence dissipation equation in the generalized relative system is presented. Simplified forms of the equation are obtained for computational purposes in the high Reynolds number approximation. Modeling of the rotation term is proposed. Modeling of the other higher-order terms is also presented in a generalized system using the tensor invariance technique. An estimate of the angular velocity is provided for the rotation term to be included in the turbulence dissipation equation. The associated significant curvature terms for turbomachinery flows are also identified.

Raj, R.↗
NASA NTRS1991

Nonaxisymmetric instabilities in rotating shear flows - Internal gravity modes in stratified media and analogies with plane flows

The role of the internal gravity modes in mediating the growth of nonaxisymmetric instabilities is investigated by studying the instability of stratified incompressible differentially rotating fluid cylinders to global nonaxisymmetric modes. The results indicate that, in addition to a modified version of the well-known principal branch mediated by surface modes of the system (analogous to f-modes of stars), there exist unstable branches of the dispersion relation mediated by internal gravity modes of the system (similar to the g-modes of stars). These branches arise due to the interaction between the g-modes. It is shown that the maximum growth rate on one of the new branches can sometimes equal or exceed that on the principal branch, thus modifying the principal branch.

Ghosh, P.↗
NASA NTRS1993

Numerical simulation of stability and stability control of high speed compressible rotating couette flow

The nonlinear temporal evolution of disturbances in compressible flow between infinitely long, concentric cylinders is investigated through direct numerical simulations of the full, three-dimensional Navier-Stokes and energy equations. Counter-rotating cylinders separated by wide gaps are considered with supersonic velocities of the inner cylinder. Initially, the primary disturbance grows exponentially in accordance with linear stability theory. As the disturbances evolve, higher harmonics and subharmonics are generated in a cascading order eventually reaching a saturation state. Subsequent highly nonlinear stages of the evolution are governed by the interaction of the disturbance modes, particularly the axial subharmonics. Nonlinear evolution of the disturbance field is characterized by the formation of high-shear layers extending from the inner cylinder towards the center of the gap in the form of jets similar to the ejection events in transitional and turbulent wall-bounded shear flows.

Biringen, Sedat↗
NASA NTRS1975

Investigation A: Numerical solutions of driven vortices of binary fluid in a cylindrical geometry

The steady state laminar motion of a viscous, incompressible and binary fluid is studied for a rotating flow in a cylindrical geometry. The mathematical model employed is a cold flow simulation of the fluid mechanics of the light-bulb concept of the gaseous core nuclear engine. A numerical treatment is developed for the rotating flow which includes a description of the nuclear fuel addition. The problem is formulated with the complete Navier-Stokes equations in order to show the interaction between the fuel addition, the main flow, and the boundary layer flow in an accurate manner. The results presented show holdup of the nuclear fuel for the case of steady fuel addition.

Shin, Y. W.↗
NASA NTRS1986

Motion and interaction of decaying trailing vortices in spanwise shear wind

A simulation is presented of the drift of trailing vortices in a cross-wind near the ground by an unsteady, two-dimensional, rotational flow field with a concentration of large vorticity in vortical spots (having a finite but small effective size and finite total strength). The problem is analyzed by a combination of the method of matched asymptotic analyses for the decay of the vortical spots and the Euler solution for the unsteady rotational flow. Using the method of averaging, a special numerical method is developed in which the grid size and time step depend only on the length and velocity scales of the background flow and are independent of the effective core size of a vortical spot. The core size can be much smaller than the grid size, whereas the peak velocity in the core is inversely propertional to the spot size. Numerical results are presented to demonstrate the strong interaction between the trajectories of the vortical spots and the change of the vorticity distribution in the background flow field.

Liu, C. H.↗
NASA NTRS1977

Computation of unsteady transonic flows through rotating and stationary cascades. 3: Acoustic far-field analysis

A small perturbation type analysis has been developed for the acoustic far field in an infinite duct extending upstream and downstream of an axial turbomachinery stage. The analysis is designed to interface with a numerical solution of the near field of the blade rows and, thereby, to provide the necessary closure condition to complete the statement of infinite duct boundary conditions for the subject problem. The present analysis differs from conventional inlet duct analyses in that a simple harmonic time dependence was not assumed, since a transient signal is generated by the numerical near-field solution and periodicity is attained only asymptotically. A description of the computer code developed to carry out the necessary convolutions numerically is included, as well as the results of a sample application using an impulsively initiated harmonic signal.

Slutsky, S.↗
NASA NTRS1982

Investigation of rotational transonic flows through ducts using a finite element scheme

An application of the finite element method is presented in order to study the flow through a two-dimensional channel including the choked and nearly-choked flow conditions. The mathematical procedure provides a combined treatment of potential and Euler equations, where the steady Euler equations are solved through the integration of a pseudo-time system which is equivalent to a relaxation scheme; the isentropic, potential flow equations are embedded in this formulation. To analyze the transonic flow through a channel with near-choked flow conditions, the flow through a parallel channel with a 10 percent circular arc bump is calculated as a sample problem.

Akay, H. U.↗