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Results for “non-dimensional numbers”

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NASA NTRS1956

On the Contribution of Turbulent Boundary Layers to the Noise Inside a Fuselage

The following report deals in preliminary fashion with the transmission through a fuselage of random noise generated on the fuselage skin by a turbulent boundary layer. The concept of attenuation is abandoned and instead the problem is formulated as a sequence of two linear couplings: the turbulent boundary layer fluctuations excite the fuselage skin in lateral vibrations and the skin vibrations induce sound inside the fuselage. The techniques used are those required to determine the response of linear systems to random forcing functions of several variables. A certain degree of idealization has been resorted to. Thus the boundary layer is assumed locally homogeneous, the fuselage skin is assumed flat, unlined and free from axial loads and the 'cabin' air is bounded only by the vibrating plate so that only outgoing waves are considered. Some of the details of the statistical description have been simplified in order to reveal the basic features of the problem. The results, strictly applicable only to the limiting case of thin boundary layers, show that the sound pressure intensity is proportional to the square of the free stream density, the square of cabin air density and inversely proportional to the first power of the damping constant and to the second power of the plate density. The dependence on free stream velocity and boundary layer thickness cannot be given in general without a detailed knowledge of the characteristics of the pressure fluctuations in the boundary layer (in particular the frequency spectrum). For a flat spectrum the noise intensity depends on the fifth power of the velocity and the first power of the boundary layer thickness. This suggests that boundary layer removal is probably not an economical means for decreasing cabin noise. In general, the analysis presented here only reduces the determination of cabin noise intensity to the measurement of the effect of any one of our variables (free stream velocity, boundary layer thickness, plate thickness or the characteristic velocity of propagation in the plate). The plate generates noise by vibrating in resonance over a wide range of frequencies and increasing the damping constant is consequently an effective method of decreasing noise generation. One of the main features of the results is that the relevant quantities upon which noise intensity depends are non-dimensional numbers in which boundary layer and plate properties enter as ratios. This is taken as an indication that in testing models of structures for boundary layer noise it is not sufficient to duplicate in the model the structural characteristics of the fuselage. One must match properly the characteristics of the exicitng pressure fluctuations to that of the structure.

Corcos, G. M.↗

NASA NTRS1990

A turbulent two-phase flow model for nebula flows

A new and very efficient turbulent two-phase flow numericaly model is described to analyze the environment of a protoplanetary nebula at a stage prior to the formation of planets. Focus is on settling processes of dust particles in flattened gaseous nebulae. The model employs a perturbation technique to improve the accuracy of the numerical simulations of such flows where small variations of physical quantities occur over large distance ranges. The particles are allowed to be diffused by gas turbulence in addition to settling under gravity. Their diffusion coefficients is related to the gas turbulent viscosity by the non-dimensional Schmidt number. The gas turbulent viscosity is determined by the means of the eddy viscosity hypothesis that assumes the Reynolds stress tensor proportional to the mean strain rate tensor. Zero- and two-equation turbulence models are employed. Modeling assumptions are detailed and discussed. The numerical model is shown to reproduce an existing analytical solution for the settling process of particles in an inviscid nebula. Results of nebula flows are presented taking into account turbulence effects of nebula flows. Diffusion processes are found to control the settling of particles.

Champney, Joelle M.↗

NASA NTRS1986

Heat and mass transfer rates during flow of dissociated hydrogen gas over graphite surface

To improve upon the performance of chemical rockets, the nuclear reactor has been applied to a rocket propulsion system using hydrogen gas as working fluid and a graphite-composite forming a part of the structure. Under the boundary layer approximation, theoretical predictions of skin friction coefficient, surface heat transfer rate and surface regression rate have been made for laminar/turbulent dissociated hydrogen gas flowing over a flat graphite surface. The external stream is assumed to be frozen. The analysis is restricted to Mach numbers low enough to deal with the situation of only surface-reaction between hydrogen and graphite. Empirical correlations of displacement thickness, local skin friction coefficient, local Nusselt number and local non-dimensional heat transfer rate have been obtained. The magnitude of the surface regression rate is found low enough to ensure the use of graphite as a linear or a component of the system over an extended period without loss of performance.

Nema, V. K.↗

NASA NTRS1990

Detailed flow-field measurements over a 75 deg swept delta wing

Results from an experimental investigation documenting the flowfield over a 75 deg swept delta wing at an angle-of-attack of 20.5 deg are presented. Results obtained include surface flow visualization, off-body flow visualization, and detailed flowfield surveys for various Reynolds numbers. Flowfield surveys at Reynolds numbers of 0.5, 1.0, and 1.5 million based on the root chord were conducted with both a Pitot pressure probe and a 5-hole pressure probe; and 3-component laser velocimeter surveys were conducted at a Reynolds number of 1.0 million. The Pitot pressure surveys were obtained at 5 chordwise stations, the 5-hole probe surveys were obtained at 3 chordwise stations and the laser velocimeter surveys were obtained at one station. The results confirm the classical roll up of the flow into a pair of primary vortices over the delta wing. The velocity measurements indicate that Reynolds number has little effect on the global structure of the flowfield for the Reynolds number range investigated. Measurements of the non-dimensional axial velocity in the core of the vortex indicate a jet like flow with values greater than twice freestream. Comparisons between velocity measurements from the 5-hole pressure probe and the laser velocimeter indicate that the pressure probe does a reasonable job of measuring the flowfield quantities where the velocity gradients in the flowfield are low.

Kjelgaard, Scott O.↗

NASA NTRS1974

Surface pressure fluctuations in hypersonic turbulent boundary layers

The surface pressure fluctuations on a flat plate model at hypersonic Mach numbers of 5.2, 7.4 and 10.4 with an attached turbulent boundary layer were measured using flush mounted small piezoelectric sensors. A high frequency resolution of the pressure field was achieved using specially designed small piezoelectric sensors that had a good frequency response well above 300 KHz. The RMS pressures and non-dimensional energy spectra for all above Mach numbers are presented. The convective velocities, obtained from space time correlation considerations are equal to 0.7 U sub infinity. The results indicate the RMS pressures vary from 5 to 25 percent of the mean static pressures. The ratios of RMS pressure to dynamic pressure are less than the universally accepted subsonic value of 6 x 10/3. The ratio decreases in value as the Mach number or the dynamic pressure is increased. The ratio of RMS pressure to wall shear for Mach number 7.4 satisfies one smaller than or equal to p/tau sub w smaller than or equal to three.

Raman, K. R.↗

NASA NTRS1983

Natural convection in an enclosed cavity

The problem of buoyancy driven flow in a vertical, rectangular cavity whose vertical sides are at different temperatures and whose horizontal sides are insulated is addressed. An application of the dynamic A.D.I. method to obtain numerical solutions to this problem is described. For large non-dimensional temperature differences characterized by the Rayleigh number the flow patterns develop strong boundary layers. These boundary layers are resolved by applying the D.A.D.I. method to the discretization of this problem on a non-uniform grid.

Phillips, T. N.↗

NASA NTRS1984

Natural convection in an enclosed cavity

Phillips, T. N.↗

NASA NTRS1989

Measurement of terms and parameters in turbulent models

Experimental measurements of the mean and turbulent velocity field in a water flow, turn-around-duct is documented. The small radius of curvature duct experiments were made over a range of Reynolds numbers (based on a duct height of 10 cm) from 70,000 to 500,000. For this particular channel, the flow is dominated by the inertia forces. Use of the local bulk velocity to non-dimensionalize the local velocity was found to limit Reynolds number effects to the regions very close to the wall. Only secondary effects on the flow field were observed when the inlet or exit boundary conditions were altered. The flow over the central two-thirds of the channel was two-dimensional. Mean tangetial and radial velocities, streamlines, pressure distributions, surface shear stress; tangential, radial and lateral turbulent velocities and the Reynolds turbulent shear values are tabulated in other reports. It is evident from the experimental study that a complex numerical modeling technique must be developed to predict the flow in the turn-around-duct. The model must be able to predict relaminarization along the inner-convex-wall. It must also allow for the major increase in turbulence produced by the outer-concave-wall.

Sandborn, Virgil A.↗

NASA NTRS1990

The analysis and simulation of compressible turbulence

Compressible turbulent flows at low turbulent Mach numbers are considered. Contrary to the general belief that such flows are almost incompressible, (i.e., the divergence of the velocity field remains small for all times), it is shown that even if the divergence of the initial velocity field is negligibly small, it can grow rapidly on a non-dimensional time scale which is the inverse of the fluctuating Mach number. An asymptotic theory which enables one to obtain a description of the flow in terms of its divergence-free and vorticity-free components has been developed to solve the initial-value problem. As a result, the various types of low Mach number turbulent regimes have been classified with respect to the initial conditions. Formulae are derived that accurately predict the level of compressibility after the initial transients have disappeared. These results are verified by extensive direct numerical simulations of isotropic turbulence.

Erlebacher, Gordon↗

NASA NTRS1989

The analysis and modeling of dilatational terms in compressible turbulence

It is shown that the dilatational terms that need to be modeled in compressible turbulence include not only the pressure-dilatation term but also another term - the compressible dissipation. The nature of these dilatational terms in homogeneous turbulence is explored by asymptotic analysis of the compressible Navier-Stokes equations. A non-dimensional parameter which characterizes some compressible effects in moderate Mach number, homogeneous turbulence is identified. Direct numerical simulations (DNS) of isotropic, compressible turbulence are performed, and their results are found to be in agreement with the theoretical analysis. A model for the compressible dissipation is proposed; the model is based on the asymptotic analysis and the direct numerical simulations. This model is calibrated with reference to the DNS results regarding the influence of compressibility on the decay rate of isotropic turbulence. An application of the proposed model to the compressible mixing layer has shown that the model is able to predict the dramatically reduced growth rate of the compressible mixing layer.

Sarkar, S.↗

NASA NTRS1991

The analysis and modelling of dilatational terms in compressible turbulence

Sarkar, S.↗

NASA NTRS1989

A parametric heat transfer study for cryogenic ball bearings in SSME HPOTP

A numerical modeling is to examine the effects of coolant convective heat transfer coefficient and frictional heating on the local temperature characteristics of a ball element in Space Shuttle Main Engine (SSME) High Pressure Oxidizer Turbopump (HPOTP) bearing. The present modeling uses a control-volume based, finite-difference method to solve the non-dimensionalized heat conduction equation in spherical coordinate system. The dimensionless temperature is found as a function of Biot number, heat flux ratio between the two race contacts, and location in the ball. The current results show that, for a given cooling capability, the ball temperature generally increases almost linearly with the heat input from the race-contacts. This increase is always very high at one of the two contacts. An increase in heat transfer coefficient generally reduces the ball temperature and alleviates the temperature gradient, except for the regions very close to the race contacts. For a 10-fold increase of heat transfer coefficient, temperature decrease is 35 percent for the average over entire ball, and 10 percent at the inner-race contact. The corresponding change of temperature gradient displays opposing trends between the regions immediately adjacent to the contacts and the remaining portion of the ball. The average temperature gradient in the vicinity of both contacts increases approximately 70 to 100 percent. A higher temperature gradient produces excessive thermal stress locally which may be detrimental to the material integrity. This, however, is the only unfavorable issue for an increase of heat transfer coefficient.

Chyu, Mingking K.↗

NASA NTRS1980

Scale effects in the dynamic transfer functions for cavitating inducers

Dynamic transfer functions for two cavitating inducers of the same geometry but different size are presented, compared and discussed. The transfer functions for each inducer indicate similar trends as the cavitation number is decreased; only minor changes are noted with changes in the flow coefficient, the uniformity of the inlet flow or the temperature of the water (21-74 C). The non-dimensional results for the two sizes are compared with themselves and with theoretical calculations based on the bubbly flow model. All three sets of results compare well and lend further credence to the theoretical model. The best values of the two parameters in the model are evaluated and recommended for use in applications.

Brennen, C. E.↗

NASA NTRS1987

Some features of surface pressure fluctuations in turbulent boundary layers with zero and favorable pressure gradients

Measurements of surface pressure fluctuation spectra, coherence and convective wave speeds from zero and favorable pressure gradient turbulent boundary layers are reported for momentum Reynolds numbers from 3000 to 18,800. The acceleration parameter K is near 2 x 10 to the -7 power for the favorable pressure gradient flow. The outer variables, U sub e, tau sub w and delta sub 1 non-dimensionalize and collapse the spectra for the low to middle range of frequencies for most test cases. The grouping using the inner variable, U sub tau and gamma, collapse the spectra for the middle to high range of frequencies for all test cases. The value of p'/tau sub w was near 3.8 and 2.8 for the smallest values of d+ in the zero and favorable pressure gradient flows, respectively. The coherence exhibits a decay that is not exponential in some cases, but the Corcos similarity parameters omega Delta x/U sub c and omega Delta z/U sub c collapse the data for all test cases. The ratio of U sub c/U sub e increases with omega delta sub 1/U sub e up to omega delta sub 1/U sub e on the order of unity, where U sub c/U sub e becomes nearly constant. This was observed in the present results for both streamwise pressure gradient flows. The experimental results presented show good agreement with previous research.

Mcgrath, B. E.↗

NASA NTRS1981

Vibrations of cantilevered shallow cylindrical shells of rectangular planform

A cantilevered, shallow shell of circular cylindrical curvature and rectangular planform exhibits free vibration behavior which differs considerably from that of a cantilevered beam or of a flat plate. Some numerical results can be found for the problem in the previously published literature, mainly obtained by using various finite element methods. The present paper is the first definitive study of the problem, presenting accurate non-dimensional frequency parameters for wide ranges of aspect ratio, shallowness ratio and thickness ratio. The analysis is based upon shallow shell theory. Numerical results are obtained by using the Ritz method, with algebraic polynomial trial functions for the displacements. Convergence is investigated, with attention being given both to the number of terms taken for each co-ordinate direction and for each of the three components of displacement. Accuracy of the results is also established by comparison with finite element results for shallow shells and with other accurate flat plate solutions.

Leissa, A. W.↗

NASA NTRS1987

Helicopter Model Rotor-Blade Vortex Interaction Impulsive Noise: Scalability and Parametric Variations

Acoustic data taken in the anechoic Deutsch-Niederlaendischer Windkanal (DNW) have documented the blade-vortex interaction (BVI) impulsive noise radiated from a 1/7-scale model main rotor of the AH-1 series helicopter. Averaged model-scale data were compared with averaged full-scale, in-flight acoustic data under similar non-dimensional test conditions using an improved data analysis technique. At low advance ratios (mu = 0.164 - 0.194), the BVI impulsive noise data scale remarkably well in level, waveform, and directivity patterns. At moderate advance ratios (mu = 0.224 - 0.270), the scaling deteriorates, suggesting that the model-scale rotor is not adequately simulating the full-scale BVI noise. Presently, no proved explanation of this discrepancy exists. Measured BVI noise radiation is highly sensitive to all of the four governing nondimensional parameters--hover tip Mach number, advance ratio, local inflow ratio, and thrust coefficient.

Boxwell, D. A.↗

NASA NTRS1984

Trailing edge flow conditions as a factor in airfoil design

Some new developments relevant to the design of single-element airfoils using potential flow methods are presented. In particular, the role played by the non-dimensional trailing edge velocity in design is considered and the relationship between the specified value and the resulting airfoil geometry is explored. In addition, the ramifications of the unbounded trailing edge pressure gradients generally present in the potential flow solution of the flow over an airfoil are examined, and the conditions necessary to obtain a class of airfoils having finite trailing edge pressure gradients developed. The incorporation of these conditions into the inverse method of Eppler is presented and the modified scheme employed to generate a number of airfoils for consideration. The detailed viscous analysis of airfoils having finite trailing edge pressure gradients demonstrates a reduction in the strong inviscid-viscid interactions generally present near the trailing edge of an airfoil.

Ormsbee, A. I.↗

NASA NTRS1991

Mixing and non-equilibrium chemical reaction in a compressible mixing layer

The effects of compressibility, chemical reaction exothermicity, and non-equilibrium chemical modeling in a reacting plane mixing layer were investigated by means of two dimensional direct numerical simulations. The chemical reaction was irreversible and second order of the type A + B yields Products + Heat. The general governing fluid equations of a compressible reacting flow field were solved by means of high order finite difference methods. Physical effects were then determined by examining the response of the mixing layer to variation of the relevant non-dimensionalized parameters. The simulations show that increased compressibility generally results in a suppressed mixing, and consequently a reduced chemical reaction conversion rate. Reaction heat release was found to enhance mixing at the initial stages of the layer growth, but had a stabilizing effect at later times. The increased stability manifested itself in the suppression or delay of the formation of large coherent structures within the flow. Calculations were performed for a constant rate chemical kinetics model and an Arrhenius type kinetic prototype. The choice of the model was shown to have an effect on the development of the flow. The Arrhenius model caused a greater temperature increase due to reaction than the constant kinetic model. This had the same effect as increasing the exothermicity of the reaction. Localized flame quenching was also observed when the Zeldovich number was relatively large.

Steinberger, Craig J.↗