Interaction between an electron wave and an ion wave due to scattering by electrons
Electron-ion wave interaction due to scattering by electrons, using kinetic wave equation to describe wave-particle interaction
Nishikawa, K.↗
SEARCH · Search NASA
Results for “kinetic equation”
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.
The structure of shock wave in a gas consisting of ideally elastic, rigid spherical molecules
Principal approaches are examined to the theoretical study of the shock layer structure. The choice of a molecular model is discussed and three procedures are formulated. These include a numerical calculation method, solution of the kinetic relaxation equation, and solution of the Boltzmann equation.
Cheremisin, F. G.↗
Prediction of free turbulent mixing using a turbulent kinetic energy method
Free turbulent mixing of two-dimensional and axisymmetric one- and two-stream flows is analyzed by a relatively simple turbulent kinetic energy method. This method incorporates a linear relationship between the turbulent shear and the turbulent kinetic energy and an algebraic relationship for the length scale appearing in the turbulent kinetic energy equation. Good results are obtained for a wide variety of flows. The technique is shown to be especially applicable to flows with heat and mass transfer, for which nonunity Prandtl and Schmidt numbers may be assumed.
Harsha, P. T.↗
Interplanetary gas dynamics.
Observations of the interplanetary medium are considered together with the structure of the solar atmosphere and the kinetic properties of the interplanetary plasma. Methods of gas kinetics and continuum flows are examined, taking into account microscopic and macroscopic representations, the kinetic flow equations, the formal solution of the Vlasov equation, and the continuum flow equations. The collective particle behavior of that interplanetary gas is discussed along with the hydrodynamic coronal expansion, a wave-pump problem, the free expansion phenomenon, and a generalized free expansion problem.
Liu, V. C.↗
Unsteady turbulent boundary layers in two-dimensional, incompressible flow.
The paper presents the results of some calculations aimed at studying the characteristics of turbulent boundary layers in unsteady flow. The calculations were performed using the method of Singleton and Nash, which is based on the turbulent kinetic energy equation. Emphasis is placed on the approach to zero wall stress, and the results show the extent to which onset of this condition can be delayed by the effects of time dependence. The delay is not associated merely with alleviation of the pressure gradients, and quasi-steady methods cannot readily be used to calculate this type of flow.
Nash, J. F.↗
Rocket engine thrust chamber heat transfer calculation and analysis
A parametric study of the heat transfer rate along the wall of a rocket nozzle is presented. The influences of different parameters; laminar and turbulent Lewis number, mixture ratio, initial wall temperature distribution, and eddy viscosity, were considered. The numerical evaluation of these influences on heat transfer rate was done by using three different compressible, reacting laminar and turbulent boundary layer computer programs; MABL (Mass Addition Boundary Layer Program), MABL-KE (MABL program is modified to include turbulent kinetic energy equation), and BLIMP (Boundary Layer Integral Matrix Procedure). This study also provided an excellent opportunity to evaluate the efficiencies of these three computer programs and to suggest one of them for future computational purposes.
Saha, H.↗
Application of a general boundary layer analysis to turbulent boundary layers subjected to strong favorable pressure gradients
Theoretical predictions of turbulent boundary layer development under the influence of strong favorable pressure gradients made using a finite-difference calculation procedure are compared to experimental data. Comparisons are presented for low speed flows with and without wall heat transfer as well as for supersonic flows with adiabatic walls. The turbulence model used is governed by an integral form of the turbulence kinetic energy equation and the results are compared with predictions made using a conventional equilibrium turbulence model based upon Prandtl's mixing length, a Clauser-type eddy viscosity model used by Cebecci and Mosinskis, and a two-equation turbulence energy model of Launder and Jones.
Kreskovsky, J. P.↗
Application of a transitional boundary-layer theory in the low hypersonic Mach number regime
An investigation is made to assess the capability of a finite-difference boundary-layer procedure to predict the mean profile development across a transition from laminar to turbulent flow in the low hypersonic Mach-number regime. The boundary-layer procedure uses an integral form of the turbulence kinetic-energy equation to govern the development of the Reynolds apparent shear stress. The present investigation shows the ability of this procedure to predict Stanton number, velocity profiles, and density profiles through the transition region and, in addition, to predict the effect of wall cooling and Mach number on transition Reynolds number. The contribution of the pressure-dilatation term to the energy balance is examined and it is suggested that transition can be initiated by the direct absorption of acoustic energy even if only a small amount (1 per cent) of the incident acoustic energy is absorbed.
Shamroth, S. J.↗
Influence of external disturbances and compressibility on free turbulent mixing
It is shown that disturbances in external flow can significantly affect, by as much as an order of magnitude, the turbulent mixing rate in free shear layers and that the length scale of the external flow disturbances is as important as the amplitude. The difference between the effect of wide-band and narrow-band disturbances is stressed. The model for pressure fluctuation term in the kinetic energy equation is included in a two-equation model. The reduced spreading rate in high Mach number, high Reynolds number, adiabatic, free turbulent shear layers is predicted.
Oh, Y. H.↗
Finite beta effects on the drift-cyclotron instability
The effects of finite plasma beta and strong plasma inhomogeneities on the microinstability resulting from the unstable coupling of ion-cyclotron oscillations and an ion drift wave are examined. A local electromagnetic, kinetic dispersion equation, which takes into account finite orbit modifications of both ions and electrons as well as the effects of strong inhomogeneities on the ions and permits the continuous tracking of the instability from the weak gradient regime to the strong gradient regime, is derived and solved numerically. Finite beta is shown to increase the frequency and reduce the growth rate of the instability, but not completely stabilize it due to electromagnetic effects. When plasma inhomogeneity is sufficiently strong, finite beta reduces the growth rate of the large k sub y band of a given harmonic more than the small k sub y band; however, the most unstable bands remain the same as in the case of zero beta. Implications of these results for the Tandem Mirror Experiment are discussed.
Gladd, N. T.↗
Premixing quality and flame stability: A theoretical and experimental study
Models for predicting flame ignition and blowout in a combustor primary zone are presented. A correlation for the blowoff velocity of premixed turbulent flames is developed using the basic quantities of turbulent flow, and the laminar flame speed. A statistical model employing a Monte Carlo calculation procedure is developed to account for nonuniformities in a combustor primary zone. An overall kinetic rate equation is used to describe the fuel oxidation process. The model is used to predict the lean ignition and blow out limits of premixed turbulent flames; the effects of mixture nonuniformity on the lean ignition limit are explored using an assumed distribution of fuel-air ratios. Data on the effects of variations in inlet temperature, reference velocity and mixture uniformity on the lean ignition and blowout limits of gaseous propane-air flames are presented.
Radhakrishnan, K.↗
Spectral analysis and diagnosis of nonlinear interactions of large-scale moving waves at 200 mb in the GLAS General Circulation Model
The space-time Fourier spectral analysis and the equations of kinetic energy and momentum transport in the wavenumber-frequency domain proposed by Kao (1968) and modified by Kao and Lee (1977) using Tukey's (1967) numerical spectral analysis are employed to analyze the 200 mb wind fields of a four-month climate experiment of the GLAS atmospheric circulation model. This climate run covers the period from Jan. 1 to Apr. 30, 1975. The current study analyzes a 90-day (Jan. 15-Apr. 14, 1975) wind field of this climate run. A comparison is conducted between the current study and observations reported by Kao and Lee. It is found that the 200 mb latitudinal distributions of model mean zonal wind, zonal and meridional kinetic energy and momentum transport of eddies agree fairly well with the observations.
Chen, T.-C.↗
Features of a reattaching turbulent shear layer in divergent channel flow
Experimental data have been obtained in an incompressible turbulent flow over a rearward-facing step in a diverging channel flow. Mean velocities, Reynolds stresses, and triple products that were measured by a laser Doppler velocimeter are presented for two cases of tunnel wall divergence. Eddy viscosities, production, convection, turbulent diffusion, and dissipation (balance of kinetic energy equation) terms are extracted from the data. These data are compared with various eddy-viscosity turbulence models. Numerical calculations incorporating the k-epsilon and algebraic-stress turbulence models are compared with the data. When determining quantities of engineering interest, the modified algebraic-stress model (ASM) is a significant improvement over the unmodified ASM and the unmodified k-epsilon model; however, like the others, it dramatically overpredicts the experimentally determined dissipation rate.
Driver, D. M.↗
Experimental study of a three-dimensional, shear-driven, turbulent boundary layer using a three-dimensional laser Doppler velocimeter
Experimental data have been obtained in a three-dimensional, shear-driven, turbulent boundary layer subjected to sudden transverse strain. Measurements made with a newly developed, three-dimensional laser Doppler velocimeter include all components of mean flow, turbulent Reynolds stresses, and triple-product correlations. Eddy viscosities, production, convection, turbulent diffusion, and dissipation (balance of kinetic energy equation) are extracted from the data. It was shown experimentally that eddy viscosity is strongly direction-dependent (not a scalar), indicating a need for full Reynolds stress modeling. Turbulence models for eddy viscosity, stress diffusion, pressure rate-of-strain, and anisotropy of Reynolds stresses are tested using the data. Calculations using a Reynolds stress equation model are compared with the data.
Driver, D. M.↗
Applications of a new wall function to turbulent flow computations
A new wall function approach is developed based on a wall law suitable for incompressible turbulent boundary layers under strong adverse pressure gradients. This wall law was derived from a one-dimensional analysis of the turbulent kinetic energy equation with gradient diffusion concept employed in modeling the near-wall shear stress gradient. Numerical testing cases for the present wall functions include turbulent separating flows around an airfoil and turbulent recirculating flows in several confined regions. Improvements on the predictions using the present wall functions are illustrated. For cases of internal recirculating flows, one modification factor for improving the performance of the k-epsilon turbulence model in the flow recirculation regions is also included.
Chen, Y. S.↗
Decoupled direct method for sensitivity analysis in combustion kinetics
An efficient, decoupled direct method for calculating the first order sensitivity coefficients of homogeneous, batch combustion kinetic rate equations is presented. In this method the ordinary differential equations for the sensitivity coefficients are solved separately from , but sequentially with, those describing the combustion chemistry. The ordinary differential equations for the thermochemical variables are solved using an efficient, implicit method (LSODE) that automatically selects the steplength and order for each solution step. The solution procedure for the sensitivity coefficients maintains accuracy and stability by using exactly the same steplengths and numerical approximations. The method computes sensitivity coefficients with respect to any combination of the initial values of the thermochemical variables and the three rate constant parameters for the chemical reactions. The method is illustrated by application to several simple problems and, where possible, comparisons are made with exact solutions and those obtained by other techniques.
Radhakrishnan, Krishnan↗
On the polarization, compression and nonoscillatory behavior of hydromagnetic waves associated with pickup ions
Solution of the kinetic dispersion equation shows that heavy pickup ions with large perpendicular energies excite a new hydromagnetic wave mode with maximum growth, high (magnetic field and mass density) compression ratios, and almost linear polarization coexisting slightly away 6-15 deg from parallel propagation. The mode arises from the coupling of the heavy ion beam to the modified left-hand wave dispersion caused by the multiion nature of the medium. The ion beam can also bring about nonoscillatory, purely growing structures distinct from the mirror wave through the coupling of a counter-streaming left-hand mode to a costreaming right-hand wave. The free energy source parameters are varied to determine their relative influence and define the domain of existence of the instability. Its characteristics may prove helpful in the interpretation of recent cometary (Halley and Giacobini-Zinner) and artificial release (AMPTE) observations.
Brinca, Armando L.↗
Turbulent separated flow in the vicinity of a single-slotted airfoil flap
Detailed measurements of pressure and velocity characteristics are presented and analyzed for flow over and downstream of a NACA 4412 airfoil equipped with a NACA 4415 single-slotted flap at high angle of attack and close to maximum lift. The flow remained attached over the main element while a large region of recirculating flow occurred over the aft 61 percent of the flap. The airfoil configuration was tested at a Mach number of 0.09 and chord based Reynolds number of 1.8 x 10 to the 6th in the NASA Ames Research Center 7- by 10-Foot Wind Tunnel. Measurements of mean and fluctuating velocities were obtained in the region of recirculation and high turbulence intensity using three-dimensional laser velocimetry. In regions where the flow had a preferred direction and relatively low turbulence intensity hot-wire anemometry was used. Emphasis was placed on obtaining flow characteristics in the confluent boundary layer, the region of recirculating flow and in the downstream wake. Surface pressure measurements were made on the main airfoil, flap, wind tunnel roof, and wind tunnel floor. In addition to the presentation of pressure and velocity characteristics, the near wall results inside the separated region are analyzed as are the relative importance of terms in the momentum and turbulence kinetic energy equations in the confluent separated boundary layer and the recirculating region of the near wake.
Adair, Desmond↗