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NASA NTRS1972

Heat transfer at reattachment of a compressible flow over a backward facing step with a suction slot.

A simplified model is suggested for engineering estimates of heat transfer in the vicinity of reattachment for the case of supersonic flow over a backward facing step with a suction slot. The presented approach gives a closed-form approximate solution which is shown to be in satisfactory agreement with experimental results for the case of no mass transfer, and is expected to predict the effect of mass transfer in the case of suction.

Telionis, D. P.↗

NASA NTRS1972

Elastic pd scattering at 316, 364, 470, and 590 MeV in the backward hemisphere.

The elastic pd differential cross section at center-of-mass angles between 91 and 164 deg was determined for 316, 364, 470, and 590 MeV proton scattering in a backward hemisphere. For the three largest energies, the cross sections were within 10% of each other at any given angle larger than 130 deg. The extrapolated 180 deg differential cross section remained nearly constant from 316 to 590 MeV.

Alder, J. C.↗

NASA NTRS1976

Turbulent atmospheric flow over a backward-facing step

The phenomenon of atmospheric shear layer separation over a man-made structure such as a building (modeled as a backward-facing step) has been analyzed theoretically by (1) solving the two-dimensional equations of motion in the two variables, stream function and vorticity, and by (2) employing an approximate integral technique. Boundary conditions for the undisturbed flow are that of the turbulent atmospheric shear flow over a rough terrain. In the first approach a two-equation model of turbulence was used. In the second approach an approximate technique was utilized in an attempt to describe the details of the flow in the recirculation zone behind the step. The results predict velocity profiles in sufficient detail that the presence of the corner eddy in the region of negative surface pressure gradient is evident. The magnitude of the reversed flow velocity in the recirculation eddy has been found to agree with that found from experiments. Also, a surface eddy viscosity distribution has been an outgrowth of the method which realistically follows the magnitude of the surface pressure gradient distribution as found experimentally.

Kaul, U. K.↗

NASA NTRS1979

Investigation of a reattaching turbulent shear layer Flow over a backward-facing step

The paper studies incompressible flow over a backward-facing step in order to investigate the flow characteristics in the separated shear layer, the reattachment zone, and the redeveloping boundary layer after reattachment. It is shown that turbulent intensities and shear stress reach maxima in the reattachment zone, followed by rapid decay near the surface after reattachment. In addition, it is found that downstream of reattachment, the flow returns very slowly to the structure of an ordinary turbulent boundary layer.

Kim, J.↗

NASA NTRS1982

Solution to the backward-Kolmogorov equation for a nonstationary oscillation problem

The transition probability density function of a Markovian approximation of the response amplitude of an oscillator under nonstationary excitation is determined in an analytical form. A solution is presented for the associated backward-Kolmogorov equation by transforming the equation into a form amenable to solution by the method of the separation of variables. This procedure results in a boundary value problem which is then solved by using an infinite series of Laguerre polynomials. It is found that the infinite series solution is equivalent to a closed-form solution involving a Bessel function.

Solomos, G. P.↗

NASA NTRS1983

Effects of expansion ratio on the calculation of parallel-walled backward-facing step flows - Comparison of four models of turbulence

This paper presents a numerical study of the effects of expansion ratio on two-dimensional separating and reattaching flows in plane backward-facing step geometries with parallel walls. Closure of the Reynolds equations was achieved by four different turbulence models: k-epsilon, 'modified' k-epsilon, algebraic stress, and 'modified' algebraic stress models. The k-epsilon model relates the Reynolds stresses to the mean rate of strain through the definition of an isotropic turbulent viscosity. The more advanced algebraic stress model calculates the stresses from implicit algebraic relationships containing the stresses themselves, the mean rate of strain, and the turbulent kinetic energy and its dissipation rate. 'Modified' versions of the models employ a new dissipation rate equation whose production term was made more sensitive to streamwise curvature effects. A new nonequilibrium wall function treatment proposed by Chieng and Launder (1980) was also incorporated into each model.

Sindir, M. M.↗

NASA NTRS1983

Computation of turbulent flows over backward-facing step

A numerical method for computing incompressible turbulent flows is presented. The method is tested by calculating laminar recirculating flows and is applied in conjunction with a modified Kappa-epsilon model to compute the flow over a backward-facing step. In the laminar regime, the computational results are in good agreement with the experimental data. The turbulent flow study shows that the reattachment length is underpredicted by the standard Kappa-epsilon model. The addition of a term to the standard model that accounts for the effects of rotation on turbulent flow improves the results in the recirculation region and increases the computed reattachment length.

Mansour, N. N.↗

NASA NTRS1984

Dielectric based submillimeter backward wave oscillator circuit

A ladder circuit especially useful in backward wave oscillators operating in the 500 GHz to 2000 GHz range has a waveguide with transversely orientated slabs which contact an upper wall of the waveguide. The edges of the slabs adjacent to the physical center of waveguide are curved segments and stubs of electrically conductive, nonmagnetic material. The ends of slabs include metal layers at opposite ends to provide a conductive leakage path. A ridge bar is attached to the inside of the bottom wall of the waveguide and includes a concave upper surface which partially straddles the electron beam. The novelty of the invention lies in the ladder structure compared of thin, vapor deposited rungs supported on the edge of diamond slabs; each rung having a curved segment which straddles the electron beam together with a ridge bar which also straddles the electron beam.

Kosmahl, H. G.↗

NASA NTRS1984

Effect of initial conditions on turbulent reattachment downstream of a backward-facing step

The reattachment of a fully turbulent, two-dimentional shear layer downstream of a backward-facing step has been studied experimentally. The work examines the effect of variations in inlet conditions on the process of reattachment. A series of experiments was conducted in a low-speed wind tunnel using specialized instrumentation suited to the highly turbulent reversing flow near reattachment. Accurate characterization of the time-mean features of the reattaching flows was possible. Assuming linear scaling normalized on distance from reattachment, distributions of normalized pressure coefficient and forward flow fraction, and time-averaged skin friction coefficient appear universal for two-dimensional reattachment, independent of initial conditions and step height, for given duct geometry (area ratio) and for high step-height Reyolds numbers with thin separating boundary layers. The results suggest universal flow structure in the reattachment zone.

Westphal, R. V.↗

NASA NTRS1986

Numerical simulation of backward step and jet exhaust flows

Preparatory to a continuing study of efficient, high resolution flow structure capture on patched mesh systems, turbulent flowfield solutions for a tactical missile base flow problem are computed on two first level composite grids of differing topologies. One mesh is of the wraparound character and the other is a step mesh on the Cartesian topology. A simplified Baldwin-Lomax algebraic eddy viscosity model is applied in the wake region. Results for the two meshes are compared with each other and with other computations reported in the literature. The totality of results suggest both mesh topology and resolution are important factors in the accuracy of predictive results as well as turbulence modeling. Related to interests in high altitude laminar flows bluff bodies such as the AOTV, the paper also presents results from a solution from laminar flow over a backward facing step and makes comparison with the available classical experiment of Chapman, et al.

Lombard, C. K.↗

NASA NTRS1985

Backward boundary layers in downward flame spread

The gas-phase combustion of a vertical fuel slab pyrolyzing at a finite rate under downward flame spread conditions is investigated theoretically. The backward boundary layer character of the flow is exploited, and a transformation that shifts the singularity associated with boundary-layer equations to a location, upstream of flame lift-off, where the surface temperature is nearly ambient, is employed. The boundary-layer flow is matched asymptotically for large Grashof number to a potential flow that allows the flow induced by the flame and along the upstream surface of the fuel bed to be calculated. Gas-phase temperature and velocity predictions are compared to experiment, and although analysis of the gas phase is emphasized, an approximate spread rate, based on a solid-phase energy balance, is calculated.

Vedha-Nayagam, M.↗

NASA NTRS1986

Triple-velocity products in a channel with a backward-facing step

Attention is given to the evaluation of tripple velocity products in the reattaching and developing region behind a backward facing step. The change in tripple velocity products is significant in the wake region, yielding substantial variation in the diffusion rate of the Reynolds stresses. Four models of the third-order closure are examined, and the results are compared with the experimental data for Chandrsuda and Bradshaw (1980).

Amano, R. S.↗

NASA NTRS1986

Laboratory measurements of forward and backward scattering of laser beams in water droplet clouds

Many aspects of the forward and backward scattering in dense water droplet clouds were studied using a laboratory scattering facility. This system is configured in a lidar geometry to facilitate comparison of the laboratory results to current lidar oriented theory and measurements. The backscatter measurements are supported with simultaneous measurements of the optical density, mass concentration, and droplet size distribution of the clouds. Measurements of the extinction and backscatter coefficients at several important laser wavelength have provided data on the relationship between these quantities for laboratory clouds at .633, 1.06, and 10.6 microns. The polarization characteristics of the backscatter of 1.06 microns were studied using several different types of clouds. More recently, the laboratory facility was modified to allow range-resolved backscatter measurements at 1.06 microns. Clouds made up of 3 layers, each with its own density, can be constructed. This allows the study of the effect of cloud inhomogeneity on the forward and backscatter.

Smith, R. B.↗

NASA NTRS1986

Finite analytic numerical solution of two-dimensional channel flow over a backward-facing step

Laminar channel flow over a backward-facing step is investigated. The finite analytic (FA) method is used to obtain the numerical solution. The FA solutions predict the recirculation zone lengths and the recirculated mass flow rates for Reynolds numbers, Re, of 25, 50, 73, 125, 191 and 229 which correlate well with experimental measurements. The general flow patterns of the recirculation region flows for the Reynolds numbers considered in this study are similar to each other.

Ho, K.-S.↗

NASA NTRS1987

Numerical solution of turbulent flow past a backward facing step using a nonlinear K-epsilon model

The problem of turbulent flow past a backward facing step is important in many technological applications and has been used as a standard test case to evaluate the performance of turbulence models in the prediction of separated flows. It is well known that the commonly used kappa-epsilon (and K-l) models of turbulence yield inaccurate predictions for the reattachment points in this problem. By an analysis of the mean vorticity transport equation, it will be argued that the intrinsically inaccurate prediction of normal Reynolds stress differences by the Kappa-epsilon and K-l models is a major contributor to this problem. Computations using a new nonlinear kappa-epsilon model (which alleviates this deficiency) are made with the TEACH program. Comparisons are made between the improved results predicted by this nonlinear kappa-epsilon model and those obtained from the linear kappa-epsilon model as well as from second-order closure models.

Speziale, C. G.↗

NASA NTRS1987

Submillimeter backward wave oscillators

A NASA program for the development of backward wave oscillators (BWOs) for the 500-2000 GHz frequency range is discussed. The BWO operation is based on a periodic etched slow wave structure which supports the induced traveling electromagnetic wave. The present submillimeter wave BWOs will employ a variation of the folded wave guide, the interdigital line. The use of a noncompressed electron beam results in less thermal loading of the circuit, smaller magnetic focusing fields, and higher current density of the circuit interaction region. The diamond etching procedure is described. Aluminum will be used for the metallization of the diamonds.

Dayton, J. A.↗

NASA NTRS1987

Investigation of third-order closure model of turbulence for the computation of incompressible flows in a channel with a backward-facing step

To predict the diffusion process of the Reynolds stresses in reattaching shear flows, the transport model for the triple-velocity products has been developed and tested for the computation of the flow in a channel with a backward-facing step. Upon comparison of the results of uuv, uvv, and vvv with those obtained by using existing algebraic correlations, it was shown that the present model improved the prediction of the triple-velocity products.

Amano, R. S.↗

NASA NTRS1988

Study of optical output couplers for submillimeter wavelength backward-wave oscillators (BWO's)

The machining of slow wave structures for high frequency backward-wave oscillators (BWO) is extremely difficult beyond 1 THz. Recently a microfabrication technique using photolithography and ion-beam assisted etching has been used to construct a prototype BWO operating at 200 to 265 GHz. The output coupler for such tubes remains a problem. Waveguides do not exist or are very lossy at the frequencies of interest (300 to 2000 GHz). This paper discusses several scaled experiments of optical output couplers for submillimeter BWOs. Various designs of planar antennas (Vivaldi horns) and lens-feed systems (Hyperhemispherical lens) were constructed and tested between 20 and 100 GHz using a spectrum analyzer. The lens system was also tested at 337 GHz using a CO2 pumped FIR laser.

Cook, Jerry D.↗