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NASA NTRSDate not supplied

Intermittency Model for Coupled CFD-Stability Transition Analysis in Hypersonic Flow

Accurate prediction of aerothermodynamic loads on hypersonic vehicles requires precise modeling of surface quantities across the boundary layer transition zone. The peak heating loads and total heat transfer are determined by parameters such as the transition zone length and the magnitude of potential overshoots in heat flux and skin friction beyond their respective values in fully turbulent flows. While previous studies on CFD integrated transition modeling using linear stability correlations have shown promise in modeling these features, they did not develop an intermittency model for hypersonic flows. This paper presents a data-driven approach to develop a model of this type by correlating experimental transition data with the relevant flow parameters. The resulting model demonstrates significant improvements over previous low-speed models in terms of predicting heat transfer distributions during the transition process associated with first and second mode instabilities in axisymmetric high-speed flows. Separate correlations for flight and ground test conditions are developed, and the potential to combine these correlations is discussed.

Transition↗

NASA NTRS1983

Turbulence analysis of the Jovian upstream 'wave' phenomenon

As Voyager 2 approached Jupiter's bow shock, large-amplitude fluctuations were seen in both the magnetic field and plasma fluid velocity. These fluctuations generally coincided with the occurrence of long-lived energetic particle events similar to the upstream waves often observed near the earth's bow shock. In this paper an analysis of the magnetic field and plasma observations using spectral methods is presented. The characteristic spectral features related to the upstream waves are generally seen near 1 mHz. The measured correlation lengths of these fluctuations suggest that they are coherent over only a few wavelengths. The analysis is consistent with the hypothesis that these fluctuations are driven by streaming ions, possibly protons. No evidence for the existence of whistler waves is found. It is argued that some of the observed spectral features suggest that dynamical turbulent processes are occurring in the uptream wave region, including a possible observation of an inverse cascade of magnetic helicity to large spatial scales.

Smith, C. W.↗

NASA NTRS2008

Deriving Lifetime Maps in the Time/Frequency Domain of Coherent Structures in the Turbulent Boundary Layer

The lifetimes of coherent structures are derived from data correlated over a 3 sensor array sampling streamwise sidewall pressure at high Reynolds number (> 10(exp 8)). The data were acquired at subsonic, transonic and supersonic speeds aboard a Tupolev Tu-144. The lifetimes are computed from a variant of the correlation length termed the lifelength. Characteristic lifelengths are estimated by fitting a Gaussian distribution to the sensors cross spectra and are shown to compare favorably with Efimtsov s prediction of correlation space scales. Lifelength distributions are computed in the time/frequency domain using an interval correlation technique on the continuous wavelet transform of the original time data. The median values of the lifelength distributions are found to be very close to the frequency averaged result. The interval correlation technique is shown to allow the retrieval and inspection of the original time data of each event in the lifelength distributions, thus providing a means to locate and study the nature of the coherent structure in the turbulent boundary layer. The lifelength data are converted to lifetimes using the convection velocity. The lifetime of events in the time/frequency domain are displayed in Lifetime Maps. The primary purpose of the paper is to validate these new analysis techniques so that they can be used with confidence to further characterize the behavior of coherent structures in the turbulent boundary layer.

Palumbo, Dan↗

NASA NTRS2007

Effect of Temperature on Jet Velocity Spectra

Statistical jet noise prediction codes that accurately predict spectral directivity for both cold and hot jets are highly sought both in industry and academia. Their formulation, whether based upon manipulations of the Navier-Stokes equations or upon heuristic arguments, require substantial experimental observation of jet turbulence statistics. Unfortunately, the statistics of most interest involve the space-time correlation of flow quantities, especially velocity. Until the last 10 years, all turbulence statistics were made with single-point probes, such as hotwires or laser Doppler anemometry. Particle image velocimetry (PIV) brought many new insights with its ability to measure velocity fields over large regions of jets simultaneously; however, it could not measure velocity at rates higher than a few fields per second, making it unsuitable for obtaining temporal spectra and correlations. The development of time-resolved PIV, herein called TR-PIV, has removed this limitation, enabling measurement of velocity fields at high resolution in both space and time. In this paper, ground-breaking results from the application of TR-PIV to single-flow hot jets are used to explore the impact of heat on turbulent statistics of interest to jet noise models. First, a brief summary of validation studies is reported, undertaken to show that the new technique produces the same trusted results as hotwire at cold, low-speed jets. Second, velocity spectra from cold and hot jets are compared to see the effect of heat on the spectra. It is seen that heated jets possess 10 percent more turbulence intensity compared to the unheated jets with the same velocity. The spectral shapes, when normalized using Strouhal scaling, are insensitive to temperature if the stream-wise location is normalized relative to the potential core length. Similarly, second order velocity correlations, of interest in modeling of jet noise sources, are also insensitive to temperature as well.

Bridges, James E.↗

NASA NTRS2007

Offset Stream Technology Test-Summary of Results

Brown, Clifford A.↗

NASA NTRS1994

An Experimental Study of the Flow Emerging from Porous Walls

The fluid mechanics of air flow exiting from porous materials is investigated. Porous walls with filter ratings differing by about three orders of magnitude are studied. The flow behavior is investigated for its spatial and temporal stability. The measurements show that coalescence effects cause jet development which gives rise to a stable, spatial velocity non-uniformity termed pseudo-turbulence. Beyond a critical mean velocity, the pseudo-turbulence shows a leveling trend and the flow exhibits jets whose dimensions are independent of wall porosity and provide a unique length scale for this type of flow field (approx. 1 mm). A correlation is developed to predict the onset of fully developed jets. The impact of using porous wall materials in cold flow solid rocket motor testing is addressed.

Ramachandran, N.↗

NASA NTRS1993

A Discrete Probability Function Method for the Equation of Radiative Transfer

A discrete probability function (DPF) method for the equation of radiative transfer is derived. The DPF is defined as the integral of the probability density function (PDF) over a discrete interval. The derivation allows the evaluation of the PDF of intensities leaving desired radiation paths including turbulence-radiation interactions without the use of computer intensive stochastic methods. The DPF method has a distinct advantage over conventional PDF methods since the creation of a partial differential equation from the equation of transfer is avoided. Further, convergence of all moments of intensity is guaranteed at the basic level of simulation unlike the stochastic method where the number of realizations for convergence of higher order moments increases rapidly. The DPF method is described for a representative path with approximately integral-length scale-sized spatial discretization. The results show good agreement with measurements in a propylene/air flame except for the effects of intermittency resulting from highly correlated realizations. The method can be extended to the treatment of spatial correlations as described in the Appendix. However, information regarding spatial correlations in turbulent flames is needed prior to the execution of this extension.

Sivathanu, Y. R.↗

NASA NTRS1952

Experimental investigation of free-convection heat transfer in vertical tube at large Grashof numbers / E. R. G. Eckert, A. J. Diaguila

Local free-convection heat-transfer coefficients and temperature fields in the turbulent flow range were obtained within a vertical, stationary tube closed at the boom, heated along its walls, and having a length-to-diameter ratio of 5. Convective heat-transfer coefficients were correlated by the general relations for free-convection heat transfer. These coefficients, converted to dimensionless Nusselt numbers were 35 percent below known relations for vertical flat plates. Air temperature measurements within the tube indicated a thin boundary layer along the heated wall surface and unstable conditions in the air flow.

HEAT TRANSFER↗

NASA NTRS1973

Calculation of free turbulent mixing by interaction approach.

The applicability of Bradshaw's interaction hypothesis to two-dimensional free shear flows was investigated. According to it, flows with velocity extrema may be considered to consist of several interacting layers. The hypothesis leads to a new expression for the shear stress which removes the usual restriction that shear stress vanishes at the velocity extremum. The approach is based on kinetic energy and the length scale equations. The compressible flow equations are simplified by restriction to low Mach numbers, and the range of their applicability is discussed. The empirical functions of the turbulence model are found here to be correlated with the spreading rate of the shear layer. The analysis demonstrates that the interaction hypothesis is a workable concept.

Morel, T.↗

NASA NTRS1972

Turbulent boundary layer on a rotating helical blade.

Investigation of the boundary-layer characteristics on a helical blade of large chord length, enclosed in an annulus and rotating in a fluid otherwise at rest. The three-dimensional form of momentum integral equations is derived, and is used to predict the boundary-layer growth and limiting streamline angles on the blade surface. The measurements are in general agreement with the predictions. The wall shear stress correlation, which includes both Reynolds number and rotation parameters, valid for a rotating blade operating at zero pressure gradient, is derived. Radial and tangential velocity profiles, the tangential component of turbulence intensity, and blade static pressures are measured at several locations on the blade surface. The nature of flow near the blade tip is discussed. An expression for the radial velocity profile, valid in the outer region of the boundary layer, is derived theoretically.

Lakshminarayana, B.↗

NASA NTRS2015

Computational Fluid Dynamics Based Extraction of Heat Transfer Coefficient in Cryogenic Propellant Tanks

Current reduced-order thermal model for cryogenic propellant tanks is based on correlations built for flat plates collected in the 1950's. The use of these correlations suffers from: inaccurate geometry representation; inaccurate gravity orientation; ambiguous length scale; and lack of detailed validation. The work presented under this task uses the first-principles based Computational Fluid Dynamics (CFD) technique to compute heat transfer from tank wall to the cryogenic fluids, and extracts and correlates the equivalent heat transfer coefficient to support reduced-order thermal model. The CFD tool was first validated against available experimental data and commonly used correlations for natural convection along a vertically heated wall. Good agreements between the present prediction and experimental data have been found for flows in laminar as well turbulent regimes. The convective heat transfer between tank wall and cryogenic propellant, and that between tank wall and ullage gas were then simulated. The results showed that commonly used heat transfer correlations for either vertical or horizontal plate over predict heat transfer rate for the cryogenic tank, in some cases by as much as one order of magnitude. A characteristic length scale has been defined that can correlate all heat transfer coefficients for different fill levels into a single curve. This curve can be used for the reduced-order heat transfer model analysis.

Yang, H. Q.↗

NASA NTRS1994

Modeling the transition region

The calculation of engineering flows undergoing laminar-turbulent transition presents special problems. Mean-flow quantities obey neither the fully laminar nor the fully turbulent correlations. In addition, local maxima in skin friction, wall temperature, and heat transfer often occur near the end of the transition region. Traditionally, modeling this region has been important for the design of turbine blades, where the transition region is long in relation to the chord length of the blade. More recently, the need for better transition-region models has been recognized by designers of hypersonic vehicles where the high Mach number, the low Reynolds number, and the low-disturbance flight environment emphasize the importance of the transition region. Needless to say, a model that might work well for the transitional flows typically found in gas turbines will not necessarily work well for the external surface of a hypersonic vehicle. In Section 2 of this report, some of the important flow features that control the transition region will be discussed. In Section 3, different approaches to the modeling problem will be summarized and cataloged. Fully turbulent flow models will be discussed in detail in Section 4; models specifically designed for transitional flow, in Section 5; and the evaluation of models, in Section 6.

Singer, Bart A.↗

NASA NTRS2015

CFD Extraction of Heat Transfer Coefficient in Cryogenic Propellant Tanks

Current reduced-order thermal model for cryogenic propellant tanks is based on correlations built for flat plates collected in the 1950's. The use of these correlations suffers from inaccurate geometry representation; inaccurate gravity orientation; ambiguous length scale; and lack of detailed validation. This study uses first-principles based CFD methodology to compute heat transfer from the tank wall to the cryogenic fluids and extracts and correlates the equivalent heat transfer coefficient to support reduced-order thermal model. The CFD tool was first validated against available experimental data and commonly used correlations for natural convection along a vertically heated wall. Good agreements between the present prediction and experimental data have been found for flows in laminar as well turbulent regimes. The convective heat transfer between the tank wall and cryogenic propellant, and that between the tank wall and ullage gas were then simulated. The results showed that the commonly used heat transfer correlations for either vertical or horizontal plate over-predict heat transfer rate for the cryogenic tank, in some cases by as much as one order of magnitude. A characteristic length scale has been defined that can correlate all heat transfer coefficients for different fill levels into a single curve. This curve can be used for the reduced-order heat transfer model analysis.

Yang, H. Q.↗

NASA NTRS1962

Measurement of Local Heat Transfer Coefficients for Flow of Hydrogen and Helium in a Smooth Tube at High Surface to Fluid Bulk Temperature Ratios

Local values of heat transfer coefficients have been measured experimentally for helium and hydrogen gas flowing through an electrically heated inconel tube. The experiment was conducted primarily to determine the effect on the heat transfer coefficient of a large density change, radially, in the heat transfer fluid. This large density change was accomplished with relatively high surface temperatures as compared to fluid bulk temperatures or more commonly referred to as high surface to fluid bulk temperature ratio. The large temperature ratio was achieved by precooling the gas with liquid nitrogen. Data were measured for local values of surface to fluid bulk temperature ratios up to 4.5, Reynolds numbers in the turbulent flow region, surface temperatures up to 2300° R, heat flux up to 1,600,000 Btu/(hr)(sq ft) and length to diameter ratio of 250. A comparison of this data with the conventional heat transfer· correlation equation (Dittus-Boelter eq.) is shown on a curve of Nusselt number divided by Prandtl number versus the Reynolds number. The gas properties were evaluated at the film temperature and the Reynolds number was modified by evaluating the velocity term at the fluid bulk temperature and the density at the film temperature.

Weiland, Walter F.↗

NASA NTRS1971

Thermal Analysis Methods and Basic Heat-Transfer Data for a Turbulent Heating Flight Experiment at Mach 20 (Reentry F)

A heat-transfer experiment was flight conducted on a 5 deg half-angle cone, 396.2 cm (13 ft) in length, as it entered the sensible atmosphere under laminar, transitional, and turbulent boundary-layer conditions at a free-stream Mach number of about 20. Accurate turbulent-heat-transfer data with natural transition were obtained for correlation with theories in regions of simultaneous high Mach number, Reynolds number, enthalpy, and total-to-wall temperature ratio. Temperatures were measured at four depths through the 15.24-mm-thick (0.600-in.) beryllium wall. Experimental heating rates at 20 stations on the cone were determined independently from the outermost temperature measurement and from the temperature measurement at the second depth by a single-thermocouple inverse method and also from the temperature histories at all four depths by an integral method. The thermal data analysis procedure, associated problems, and results are presented herein.

Howard, Floyd G.↗

NASA NTRS1972

Discrete sonic jets used as boundary-layer trips at Mach numbers of 6 and 8.5

The effect of discrete three-dimensional sonic jets used to promote transition on a sharp-leading-edge flat plate at Mach numbers of 6 and 8.5 and unit Reynolds numbers as high as 2.5 x 100,000 per cm in the Langley 20-inch hypersonic tunnels is discussed. An examination of the downstream flow-field distortions associated with the discrete jets for the Mach 8.5 flow was also conducted. Jet trips are found to produce lengths of turbulent flow comparable to those obtained for spherical-roughness-element trips while significantly reducing the downstream flow distortions. A Reynolds number based upon secondary jet penetration into a supersonic main flow is used to correlate jet-trip effectiveness just as a Reynolds number based upon roughness height is used to correlate spherical-trip effectiveness. Measured heat-transfer data are in agreement with the predictions.

Stone, D. R.↗

NASA NTRS1977

An experimental investigation of a three dimensional wall jet

One and two point statistical properties are measured in the flow fields of a coflowing turbulent jet. Two different confining surfaces (one flat, one with large curvature) are placed adjacent to the lip of the circular nozzle; and the resultant effects on the flow field are determined. The one point quantities measured include mean velocities, turbulent intensities, velocity and concentration autocorrelations and power spectral densities, and intermittencies. From the autocorrelation curves, the Taylor microscale and the integral length scale are calculated. Two point quantities measured include velocity and concentration space-time correlations and pressure velocity correlations. From the velocity space-time correlations, iso-correlation contours are constructed along with the lines of maximum maximorum. These lines allow a picture of the flow pattern to be determined. The pressures monitored in the pressure velocity correlations are measured both in the flow field and at the surface of the confining wall(s).

Catalano, G. D.↗

NASA NTRS1976

Autocorrelation peaks in congruential pseudorandom number generators

The complete correlation structure of several congruential pseudorandom number generators (PRNG) of the same type and small cycle length was studied to deal with the problem of congruential PRNG almost repeating themselves at intervals smaller than their cycle lengths, during simulation of bandpass filtered normal random noise. Maximum period multiplicative and mixed congruential generators were studied, with inferences drawn from examination of several tractable members of a class of random number generators, and moduli from 2 to the 5th power to 2 to the 9th power. High correlation is shown to exist in mixed and multiplicative congruential random number generators and prime moduli Lehmer generators for shifts a fraction of their cycle length. The random noise sequences in question are required when simulating electrical noise, air turbulence, or time variation of wind parameters.

Neuman, F.↗