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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

A hybrid computational approach to multiple-body viscous flow problems - Application to large-eddy breakup in a boundary layer

By combining stream-function and integral-velocity formulations, the hybrid computational procedure is rendered applicable to unsteady, two-dimensional flows about multiple bodies; the bodies in the flow are replaced by distributions of bound vorticity over their surfaces. By expressing the rotational velocity field generated by the free vorticity in terms of the stream function, stream function boundary conditions are required only on the periphery of the computational domain. The procedure is employed in the simulation of coherent eddy breakup by a single flat plate that is embedded in a viscous boundary layer, exhibiting significant unsteady flow features through the graphical presentation of vorticity contours.

Kinney, R. B.↗
NASA NTRS1944

Gas Jets

A brief summary of the contents of this paper is presented here. In part I the differential equations of the problem of a gas flow in two dimensions is derived and the particular integrals by which the problem on jets is solved are given. Use is made of the same independent variables as Molenbroek used, but it is found to be more suitable to consider other functions. The stream function and velocity potential corresponding to the problem are given in the form of series. The investigation on the convergence of these series in connection with certain properties of the functions entering them forms the subject of part II. In part III the problem of the outflow of a gas from an infinite vessel with plane walls is solved. In part IV the impact of a gas jet on a plate is considered and the limiting case where the jet expands to infinity changing into a gas flow is taken up in more detail. This also solved the equivalent problem of the resistance of a gaseous medium to the motion of a plate. Finally, in part V, an approximate method is presented that permits a simpler solution of the problem of jet flows in the case where the velocities of the gas (velocities of the particles in the gas) are not very large.

Chaplygin, S.↗
NASA NTRS1945

Graphical and analytical methods for the determination of a flow of a compressible fluid around an obstacle

Chaplygin introduced the hodograph method in the theory of compressible fluid flows and developed a method for constructing stream functions of such flows. This method, which has been extensively used in investigation of compressible fluid flows, is limited in certain respects. The expression for the stream function obtained in this manner can represent only certain types of flow patterns. In general, flow patterns obtained in this way cannot represent the whole flow around an obstacle, but only a part of such a flow, and therefore several expressions are needed in order to obtain the whole flow. On the other hand, in many instances it is important to have a single expression representing the whole flow. Recently Von Karman and Tsien constructed more general types of stream functions, but only by replacing the true pressure density relation by the linear pressure-specific volume relation so that their method is essential limited to flows the maximum Mach number of which is not too large. In a companion report the author derived a new formula for stream functions based on the true pressure density relation. It is not subject to the limitations of the Chaplygin method. In the present report this formula is employed to construct two-dimensional subsonic compressible fluid flows around a body similar in shape to a given symmetric obstacle. The methods described in the report are illustrated by numerical examples.

FLOW, COMPRESSIBLE-MEASUREMENT↗
NASA NTRS1987

A method of calculating the total flow from a given sea surface topography

Using a simple dynamical model of a wind-driven ocean circulation of the Stommel type, and an analytical basis developed to objectively analyze the sea surface height residuals from an altimeter and, in the process, to determine the total flow instead of just the near surface geostrophic component associated with the given sea surface topography. The method is based on first deriving the solution to the forced problem for a given wind stress required to develop a hypothetical true or perfect data field and to establishing the basis for the objective analysis. The stream function and the surface height field for the forced problem are developed in terms of certain characteristic functions with the same expansion coefficients for both fields. These characteristic functions are simply the solutions for a homogeneous elliptic equation for the stream function and the solutions of an inhomogeneous balance equation for the height field. For the objective analysis, using a sample of randomly selected height values from the true data field, the height field characteristic functions are used to fit the given topography in a least squares sense. The resulting expansion coefficients then permit the synthesis of the total flow field via the stream function characteristic modes and the solution is perfectly well behaved even along the equator. The method of solution is easily adaptable to realistic ocean basis by straight forward numerical methods. The analytical basis of the theory and the results for an ideal rectangular basin on a beta plane are described.

Rao, Desiraju B.↗
NASA NTRS2011

Comparison of Four Mixed Layer Mesoscale Parameterizations and the Equation for an Arbitrary Tracer

In this paper we discuss two issues, the inter-comparison of four mixed layer mesoscale parameterizations and the search for the eddy induced velocity for an arbitrary tracer. It must be stressed that our analysis is limited to mixed layer mesoscales since we do not treat sub-mesoscales and small turbulent mixing. As for the first item, since three of the four parameterizations are expressed in terms of a stream function and a residual flux of the RMT formalism (residual mean theory), while the fourth is expressed in terms of vertical and horizontal fluxes, we needed a formalism to connect the two formulations. The standard RMT representation developed for the deep ocean cannot be extended to the mixed layer since its stream function does not vanish at the ocean's surface. We develop a new RMT representation that satisfies the surface boundary condition. As for the general form of the eddy induced velocity for an arbitrary tracer, thus far, it has been assumed that there is only the one that originates from the curl of the stream function. This is because it was assumed that the tracer residual flux is purely diffusive. On the other hand, we show that in the case of an arbitrary tracer, the residual flux has also a skew component that gives rise to an additional bolus velocity. Therefore, instead of only one bolus velocity, there are now two, one coming from the curl of the stream function and other from the skew part of the residual flux. In the buoyancy case, only one bolus velocity contributes to the mean buoyancy equation since the residual flux is indeed only diffusive.

Canuto, V. M.↗
NASA NTRS1977

A high Reynolds number numerical solution of the Navier-Stokes equations in stream function-vorticity form

Problems encoutered in investigations of high Reynolds number, incompressible flow are reviewed. A numerical solution computer program was modified to solve the stream function-vorticity form of the Navier-Stokes equations. Using a body fitted coordinate system with a U-shaped outer boundary, a simulation of incompressible flow at a Reynolds number of one million and a body angle of attack of zero was achieved.

Bearden, J. H.↗
NASA NTRS1991

Ocean data assimilation using optimal interpolation with a quasi-geostrophic model

A quasi-geostrophic (QG) stream function is analyzed by optimal interpolation (OI) over a 59-day period in a 150-km-square domain off northern California. Hydrographic observations acquired over five surveys were assimilated into a QG open boundary ocean model. Assimilation experiments were conducted separately for individual surveys to investigate the sensitivity of the OI analyses to parameters defining the decorrelation scale of an assumed error covariance function. The analyses were intercompared through dynamical hindcasts between surveys. The best hindcast was obtained using the smooth analyses produced with assumed error decorrelation scales identical to those of the observed stream function. The rms difference between the hindcast stream function and the final analysis was only 23 percent of the observation standard deviation. The two sets of OI analyses were temporally smoother than the fields from statistical objective analysis and in good agreement with the only independent data available for comparison.

Rienecker, Michele M.↗
NASA NTRS1996

Heat and Momentum Transfer Studies in High Reynolds Number Wavy Films at Normal and Reduced Gravity Conditions

We examined the effect of the gas flow on the liquid film when the gas flows in the countercurrent direction in a vertical pipe at normal gravity conditions. The most dramatic effect of the simultaneous flow of gas and liquid in pipes is the greatly increased transport rates of heat, mass, and momentum. In practical situations this enhancement can be a benefit or it can result in serious operational problems. For example, gas-liquid flow always results in substantially higher pressure drop and this is usually undesirable. However, much higher heat transfer coefficients can be expected and this can obviously be of benefit for purposes of design. Unfortunately, designers know so little of the behavior of such two phase systems and as a result these advantages are not utilized. Due to the complexity of the second order boundary model as well as the fact that the pressure variation across the film is small compared to the imposed gas phase pressure, the countercurrent gas flow affect was studied for the standard boundary layer model. A different stream function that can compensate the shear stress affect was developed and this stream function also can predict periodic solutions. The discretized model equations were transformed to a traveling wave coordinate system. A stability analysis of these sets of equations showed the presence of a Hopf bifurcation for certain values of the traveling wave velocity and the shear stress. The Hopf celerity was increased due to the countercurrent shear. For low flow rate the increases of celerity are more than for the high flow rate, which was also observed in experiments. Numerical integration of a traveling wave simplification of the model also predicts the existence of chaotic large amplitude, nonperiodic waves as observed in the experiments. The film thickness was increased by the shear.

Balakotaiah, V.↗
NASA NTRS1947

Equations for Adiabatic but Rotational Steady Gas Flows without Friction

This paper makes the following assumptions: 1) The flowing gases are assumed to have uniform energy distribution. ("Isoenergetic gas flows," that is valid with the same constants for the the energy equation entire flow.) This is correct, for example, for gas flows issuing from a region of constant pressure, density, temperature, end velocity. This property is not destroyed by compression shocks because of the universal validity of the energy law. 2) The gas behaves adiabatically, not during the compression shock itself but both before and after the shock. However, the adiabatic equation (p/rho(sup kappa) = C) is not valid for the entire gas flow with the same constant C but rather with an appropriate individual constant for each portion of the gas. For steady flows, this means that the constant C of the adiabatic equation is a function of the stream function. Consequently, a gas that has been flowing "isentropically",that is, with the same constant C of the adiabatic equation throughout (for example, in origination from a region of constant density, temperature, and velocity) no longer remains isentropic after a compression shock if the compression shock is not extremely simple (wedge shaped in a two-dimensional flow or cone shaped in a rotationally symmetrical flow). The solution of nonisentropic flows is therefore an urgent necessity.

Schaefer, Manfred↗
NASA NTRS1984

Programs for calculating quasi-three-dimensional flow in a turbomachine blade row

MERIDL is a program that calculates a meridional plane stream function solution, and TSONIC is a program that calculates a blade to blade stream function solution for turbomachine blade passages. Both programs are discussed, including input required and assumptions and limitations. Examples of use and references are included.

Katsanis, T.↗