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At least 685 records · Page 38

Flow of rarefied gases over two-dimensional bodies

A kinetic-theory analysis is made of the flow of rarefied gases over two-dimensional bodies of arbitrary curvature. The Boltzmann equation simplified by a model collision integral is written in an arbitrary orthogonal curvilinear coordinate system, and solved by means of finite-difference approximation with the discrete ordinate method. A numerical code is developed which can be applied to any two-dimensional submerged body of arbitrary curvature for the flow regimes from free-molecular to slip at transonic Mach numbers. Predictions are made for the case of a right circular cylinder.

Jeng, Duen-Ren↗

Stability analysis of the accretion line

The stability of the flow along the accretion line in the Bondi-Hoyle-Lyttleton-type accretion flow is studied. The WKB approximation is used to analyze short wavelength linear perturbations of the axisymmetric steady state flow. The viscosity terms in the gasdynamical equations are included in the analysis. The radial modes are studied both in two- and three-dimensional accretion flow. Since a displaced accretion line cannot be defined in three-dimensional flow, the tangential modes are only analyzed in the two-dimensional flow. The analysis of the perturbed gasdynamical equations are made simpler as a result of the radial and tangential modes being decoupled in the linear regime. As was shown before, the three-dimensional accretion flow is unstable against radial modes. The two-dimensional accretion flow is found to be unstable against tangential modes, as well as against radial modes. Using typical numerical parameters which are in common use, the wavelength which gives the maximum growth rate of a small perturbation is found to be about 0.5 r(a), where r(a) is the accretion radius.

Soker, Noam↗

Vertical extensions of galactic spiral arms

The vertical structure of the large scale galactic shock along spiral arms is studied in order to understand the extended features or the wings of spiral arms observed by Kepner (1970) and recently checked by Soukup (1979). Numerical calculations of two-dimensional gas flow were performed for two models of the gas. The results show that the shock front, standing perfectly perpendicular to the galactic plane, extends impressively above the scale height of the interstellar gas. In the extreme case of isothermal gas, the shock solution exists at any distance from the plane. In a realistic model in which the kinetic temperature of the gas is stratified, increasing with height, the shock can extend up to 700 pc. For both models, although the velocity component perpendicular to the galactic plane is small, the solutions corresponding to layered one-dimensional flow contain no shocks at such heights. In order to study the geometry of the shock front and the flow pattern near it, a simplified model is adopted, in which the Coriolis force is neglected. However, estimates show that including it will enhance the shock strength. The compression at the shock front makes the gas observable at high latitudes.

Soukup, J. E.↗

Asymmetric two-dimensional jet efflux from a channel

Irrotational flow of two-dimensional jets from a channel is treated without direct use of a logarithmic hodograph plane. An analytical approach is introduced for solving the general problem of two jets issuing from a channel with three end plates. Numerical values of the contraction coefficient and the angle of jet deflection are obtained for the special case where the two jets are located symmetrically and all the end plates are in line. Limiting cases of the resulting single-jet problem are the symmetric and asymmetric configurations solved by von Mises (1917). Results for the asymmetric case improve upon the theoretical values reported by von Mises and compare favorably with existing experimental data.

Martin, C. S.↗

A viscous-inviscid interactive procedure for rotational flow in cascades of two-dimensional airfoils of arbitrary shape

A viscous-inviscid interactive calculation procedure is developed for application to flow in cascades of two-dimensional airfoils. This procedure has essentially three components. First, a numerical solution of the Euler equations which can accommodate an arbitrarily specified cascade geometry is carried out on a nonorthogonal curvileanear grid mesh that is fitted to the geometry of the cascade. A method of grid generation has been used which relies in part on a succession of conformal mappings. Second, a viscous solution for use in boundary layer and wake regions has been programmed. Finally, an interactive scheme which takes the form of a source-sink distribution along the blade surface and wake centerline is employed. Results have been obtained with this procedure for several cascade flow situations, and some comparisons with experiment are presented.

Johnston, W.↗

Shock-free configurations in two-and three-dimensional transonic flow

Efforts to replace Sobieczky's complicated analog computations of solutions to the hodograph equations by a fast elliptic solver in order to generate shock-free airfoil designs more effectively are described. The indirect design of airfoil and wing shapes that are free from shock waves even though the local flow velocity exceeds the speed of sound is described. The problem of finding an airfoil in two dimensional, irrotational flow that has a prescribed pressure distribution is as addressed. Sobieczky's suggestion to use a fictitious gas for finding shock-free airfoils directly in the physical plane was the basis for a more efficient procedure for achieving the same end.

Seebass, A. R.↗

Methane Hydrate Formation in Thick Sandstones by Free Gas Flow

We show with a two-dimensional multiphase flow and multicomponent transport model that free gas flow is a viable mechanism to form concentrated methane hydrate in meter-scale, dipping sandstones far above the base of the hydrate stability zone (BHSZ). In this model, gas preferentially flows updip along the top of sandstone due to buoyancy. This drives hydrate formation, increasing the local salinity to the stability limit and developing three-phase (gas, liquid, and hydrate) equilibrium above the BHSZ. With time, the gas and the hydrate solidification front (HSF) advance together updip. Behind the HSF, hydrate continues to form as the elevated salinity diffuses away. High hydrate saturations reduce the sediment permeability significantly. As a result, as the gas and HSF move updip, they are also pushed perpendicularly from the top to the base of the sandstone. The hydrate system ultimately self-seals itself due to reduced permeability across the entire thickness of the sandstone. Gas starts to retreat downdip and accumulates below the BHSZ. With this model high hydrate saturations form far above the BHSZ at high methane supply rates while hydrate is concentrated at the BHSZ or no hydrate forms at low methane supply rates. This study provides further insights into hydrate formation by free gas flow, which can be used to design the best strategies for economic and environmental production of methane from hydrate reservoirs.

58 GEOSCIENCES↗

Experimental study of flow about a stalled two-dimensional airfoil

Wind tunnel tests to determine the flow characteristics of a stalled wing are described. The advantages of the plane wing over the ring wing for wind tunnel investigations are presented. The general flow pattern for stalled ring airfoils is developed. Photographs of the test equipment and installation are provided.

Coles, D. E.↗

Laminar/turbulent oscillating flow in circular pipes

A two-dimensional oscillating flow analysis was conducted simulating the gas flow inside Stirling engine heat exchangers. Both laminar and turbulent oscillating pipe flow were investigated numerically for Re(max) = 1920 (Va = 80), 10,800 (Va = 272), 19,300 (Va = 272), and 60,800 (Va = 126). The results are compared with experimental results of previous investigators. Predictions of the flow regime are also checked by comparing velocity amplitudes and phase difference with those from laminar theory and quasi-steady profile. A high Reynolds number k-epsilon turbulence model was used for turbulent oscillating pipe flow. Finally, the performance of the k-epsilon model was evaluated to explore the applicability of quasi-steady turbulent models to unsteady oscillating flow analysis.

Ahn, Kyung H.↗

An upwind, kinetic flux-vector splitting method for flows in chemical and thermal non-equilibrium

We have developed new upwind kinetic difference schemes for flows with non-equilibrium thermodynamics and chemistry. These schemes are derived from the Boltzmann equation with the resulting Euler schemes developed as moments of the discretized Boltzmann scheme with a locally Maxwellian velocity distribution. Splitting the velocity distribution at the Boltzmann level is seen to result in a flux-split Euler scheme and is called Kinetic Flux Vector Splitting (KFVS). Extensions to flows with finite-rate chemistry and vibrational relaxation is accomplished utilizing nonequilibrium kinetic theory. Computational examples are presented comparing KFVS with the schemes of Van Leer and Roe for a quasi-one-dimensional flow through a supersonic diffuser, inviscid flow through two-dimensional inlet, and viscous flow over a cone at zero angle-of-attack. Calculations are also shown for the transonic flow over a bump in a channel and the transonic flow over an NACA 0012 airfoil. The results show that even though the KFVS scheme is a Riemann solver at the kinetic level, its behavior at the Euler level is more similar to the existing flux-vector splitting algorithms than to the flux-difference splitting scheme of Roe.

Eppard, W. M.↗

Velocity, temperature, and electrical conductivity profiles in hydrogen-oxygen MHD duct flows

This paper presents results of two-dimensional duct flow computations for radial distributions of velocity, temperature, and electrical conductivity. Calculations were carried out for the flow conditions representative of NASA Lewis hydrogen-oxygen combustion driven MHD duct. Results are presented for two sets of computations: (1) profiles of developing flow in a smooth duct, and (2) profiles of fully developed pipe flow with a specified streamwise shear stress distribution. The predicted temperature and electrical conductivity profiles for the developing flows compared well with available experimental data.

Greywall, M. S.↗

Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow.

Experiments on fully developed turbulent flow in a channel which is rotating at a steady rate about a spanwise axis are described. The Coriolis force components in the region of two-dimensional mean flow affect both local and global stability. Three stability-related phenomena were observed or inferred: (1) the reduction (increase) of the rate of wall-layer streak bursting in locally stabilized (destabilized) wall layers; (2) the total suppression of transition to turbulence in a stabilized layer; (3) the development of large-scale roll cells on the destabilized side of the channel by growth of a Taylor-Gortler vortex instability. Local effects of rotational stabilization, such as reduction of the turbulent stress in wall layers, can be related to the local Richardson number in a simple way. This paper not only investigates this effect, but also, by methods of flow visualization, exposes some of the underlying structure changes caused by rotation.-

Johnston, J. P.↗

Integral boundary-layer models for turbulent separated flows

Two-dimensional, integral boundary-layer methods of the entrainment and dissipation type, with closure relationships which account for turbulent separated flows through the velocity and turbulence models, are developed. Kinematic shape factor relations used in the two methods are evaluated by comparison with recently obtained experimental data for separated flows. Prescribed-displacement-thickness computations are made with both methods and compared to experiment for a series of separated flows, including low speed and transonic shock-induced separation. Effects of upstream history on the turbulent shear stress development are shown to be important for the accurate prediction of the separated flows considered and the experimental trends are reasonably modeled by a rate equation derived from the turbulent kinetic energy equation.

Thomas, J. L.↗

A two-step scheme for the advection equation with minimized dissipation and dispersion errors

A two-step advection scheme of the Lax-Wendroff type is derived which has accuracy and phase characteristics similar to that of a third-order scheme. The scheme is exactly third-order accurate in time and space for uniform flow. The new scheme is compared with other currently used methods, and is shown to simulate well the advection of localized disturbances with steep gradients. The scheme is derived for constant flow and generalized to two-dimensional nonuniform flow.

Takacs, L. L.↗

A viscous-inviscid interaction method for ejectors having two primary jets

A viscous-inviscid interaction methodology is developed for evaluating the performance of two-dimensional incompressible flow ejectors that utilize two primary jets. In this method, the inviscid portion of the flow field, which contains the ambient fluid drawn into the device, is modeled using a higher-order panel method. The viscous region, which contains the turbulent jets, is described by an integral method. The viscous and inviscid solutions are matched together in an iterative process that simulates the interaction between the jets and the ambient fluid. The model is applied to a variety of parametric and optimization studies that illustrate the connection between the details of the ejector geometry and the level of thrust augmentation. The advantages of a dual-jet configuration are assessed through comparison with similar calculations for an otherwise identical single-jet ejector.

Lund, T. S.↗

Computation of turbulent flow in a thin liquid layer of fluid involving a hydraulic jump

Numerically computed flow fields and free surface height distributions are presented for the flow of a thin layer of liquid adjacent to a solid horizontal surface that encounters a hydraulic jump. Two kinds of flow configurations are considered: two-dimensional plane flow and axisymmetric radial flow. The computations used a boundary-fitted moving grid method with a k-epsilon model for the closure of turbulence. The free surface height was determined by an optimization procedure which minimized the error in the pressure distribution on the free surface. It was also checked against an approximate procedure involving integration of the governing equations and use of the MacCormack predictor-corrector method. The computed film height also compared reasonably well with previous experiments. A region of recirculating flow was found to be present adjacent to the solid boundary near the location of the jump, which was caused by a rapid deceleration of the flow.

Rahman, M. M.↗