Theoretical and experimental investigation of random gust loads Part II : theoretical formulation of atmospheric gust response problem
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Richardson, A S , Jr↗
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Comparing Theoretically Scaled Biomechanical Models
BACKGROUND An investigation into incorporating space suit aspects required a 50th-percentile male model which was not part of the existing dataset of models. Previously, theoretical models for 5th-percentile female and 95th-percentile male were created utilizing a scaled test subject as close as possible to the target height and weight. Scaling factors were created by taking the height ratio and applying it uniformly to the model body segments, then fine tuning to ensure the theoretical model’s height is as expected. This study was initiated to examine the existing method of isometrically scaling in OpenSim [1,2] and to create alternative methods which do not rely on an existing subject being close in height and weight to the theoretical model of interest. Generating a theoretical biomechanical model provides additional abilities without the reliance on available OpenSim models or real subjects. Gained abilities include creating different percentile models and attaining representative anthropometry for any target height/weight, such as targeting specific crew populations or gaps within the current dataset. METHODS AND RESULTS This study includes 3 methods for generating the theoretical model; utilizing the modified unscaled OpenSim Full Body Rajagopal Model (FBRM) [3,4], a dataset of scaled OpenSim models, and existing scaling factors from Dumas et al. [5]. All methods use the Anthropometric Survey of US Army Personnel (ANSUR II) [6] as an input of necessary anthropometric measurements. The following measurements are retrieved from the ANSUR II collection: mass, stature, cervicale height, acromial height, axilla height, waist height, trochanterion height, lateral femoral epicondyle height, lateral malleolus height, acromion-radiale length, radiale-stylion length, palm length, ball of foot length, bicristal breadth, bimalleolar breadth. Some of the measurements are direct segment lengths and others are utilized to derive segment lengths. Height, weight, and age ranges are the required inputs to parse the collection for a mean value of the measurements. A simple iterative process may be necessary for the output of mean mass and stature consistent with the theoretical model of interest. In some cases, one may specify exact values instead of a range but that is dependent upon whether those exact values pertain to a single subject from the ANSUR II collection. Equations from Dumas et al. were used to calculate scaling factors for the two methods that utilize OpenSim scaled and unscaled models. In the third method, Dumas’ scaling factors were used directly instead of generating our own. After scaling factors are achieved, they are applied along with the mass and segment lengths retrieved from ANSUR II in order to calculate the segment mass, Center of Mass (CoM), mass Moment of Inertia (MoI), and the joint location in the parent frame. The theoretical models from the different methods were compared to the previous existing method of isometrically scaling in OpenSim, as well as the standards found in NASA STD-3000 [7] and the NASA Human Integration Design Handbook [8]. The whole-body center of mass is the main comparison performed between the models and the standards. The body segment mass properties were also compared when possible. In some cases, the standards do not provide complete data, or the center of mass location is not provided with respect to the appropriate joint coordinate system. For a 50th-percentile male subject, results from isometric scaling in OpenSim and the method utilizing the unscaled FBRM were compared to the standards in NASA STD-3000. According to the standard, the whole-body vertical CoM location was taken from the head vertex to the CoM. The standards provide 80.2 cm for the CoM vertical component whereas isometric scaling in OpenSim and utilizing the unscaled FBRM provide 82.2 and 82.3 cm, respectively. Through definition, the whole-body CoM in the medial/lateral direction agreed across the models. Investigation is on-going to clearly identify the reference point pertaining to dorsal/ventral whole-body CoM position in standards and relate that to the theoretical models. REFERENCES [1] Delp, S.L., et al., “OpenSim: Open-source Software to Create and Analyze Dynamic Simulations of Movement”, IEEE Transactions on Biomedical Engineering, (2007). [2] Seth, A., Hicks J.L., Uchida, T.K., Habib, A., Dembia, C.L., Dunne, J.J., Ong, C.F., DeMers, M.S., Rajagopal, A., Millard, M., Hamner, S.R., Arnold, E.M., Yong, J.R., Lakshmikanth, S.K., Sherman,n M.A., Delp, S.L. OpenSim: Simulating musculoskeletal dynamics and neuromuscular control to study human and animal movement. Plos Computational Biology, 14(7). (2018) [3] R. K. Huffman, W. K. Thompson, C. A. Gallo, L. J. Quiocho, “Improvement of Scaling and Inverse Kinematic Results with Additional Upper Body Joints Added to Opensim Rajagopal Model”, NASA Human Research Program Investigator’s Workshop, (2019). [4] Huffman R.K., Thompson W., Gallo C., “Modified OpenSim Rajagopal Full Body Model”, New Technology Report, MSC-26872-1. (August 2020). [5] Dumas R., Cheze L. and Verriest J., 2007. “Adjustments to McConville et al. and Young et al. body segment inertial parameters”. Journal of Biomechanics 40, pp. 543-553 [6] Gordon C.C., 2012 “Anthropometric Survey of U.S. Army Personnel: Methods and Summary Statistics”, US Army Natick Soldier RD&E Center. [7] NASA STD-3000/REV-B, 1995. “The Man-System Integration Standards” [8] NASA/SP-2010-3407/REV-1, 2014. “The Human Integration Design Handbook (HIDH)”
F N Matari↗
An experimental-theoretical study of free vibrations of plates on elastic point supports
A theoretical and experimental study is made to investigate the effect on plate vibrations of varying the stiffness of corner elastic point supports. A theoretical model is developed using a Rayleigh-Ritz analysis which approximates the plate mode shapes as products of free-free beam modes. The elastic point supports are modelled both as massless translational springs, and springs with tip masses. The tip masses are included to better represent the experimental supports. An experiment is constructed using the bending stiffness of horizontal beams to support a square plate at its four corners. The stiffness of these supports can be varied over such a range that the plate fundamental frequency is lowered to 40% of the rigid support frequency. The variation with support stiffness of the frequencies of the first eight plate modes is measured, and compared with the theoretical results. The plate mode shapes for rigid supports are analyzed using holographic interferometry. There is excellent agreement between the theoretical and experimental results, except for high plate modes where the theoretical model is demonstrated to be inadequate.
Leuner, T. R.↗
Comparison of experimental and theoretical reaction rail currents, rail voltages, and airgap fields for the linear induction motor research vehicle
Measurements of reaction rail currents, reaction rail voltages, and airgap magnetic fields in tests of the Linear Induction Motor Research Vehicle (LIMRV) were compared with theoretical calculations from the mesh/matrix theory. It was found that the rail currents and magnetic fields predicted by the theory are within 20 percent of the measured currents and fields at most motor locations in most of the runs, but differ by as much as a factor of two in some cases. The most consistent difference is a higher experimental than theoretical magnetic field near the entrance of the motor and a lower experimental than theoretical magnetic field near the exit. The observed differences between the theoretical and experimental magnetic fields and currents do not account for the differences of as much as 26 percent between the theoretical and experimental thrusts.
Elliott, D. G.↗
A common geometric data-base approach for computer-aided manufacturing of wind-tunnel models and theoretical aerodynamic analysis
A more automated process to produce wind tunnel models using existing facilities is discussed. A process was sought to more rapidly determine the aerodynamic characteristics of advanced aircraft configurations. Such aerodynamic characteristics are determined from theoretical analyses and wind tunnel tests of the configurations. Computers are used to perform the theoretical analyses, and a computer aided manufacturing system is used to fabricate the wind tunnel models. In the past a separate set of input data describing the aircraft geometry had to be generated for each process. This process establishes a common data base by enabling the computer aided manufacturing system to use, via a software interface, the geometric input data generated for the theoretical analysis. Thus, only one set of geometric data needs to be generated. Tests reveal that the process can reduce by several weeks the time needed to produce a wind tunnel model component. In addition, this process increases the similarity of the wind tunnel model to the mathematical model used by the theoretical aerodynamic analysis programs. Specifically, the wind tunnel model can be machined to within 0.008 in. of the original mathematical model. However, the software interface is highly complex and cumbersome to operate, making it unsuitable for routine use. The procurement of an independent computer aided design/computer aided manufacturing system with the capability to support both the theoretical analysis and the manufacturing tasks was recommended.
See, M. J.↗
Clusters of DNA induced by ionizing radiation: formation of short DNA fragments. I. Theoretical modeling
We have developed a general theoretical model for the interaction of ionizing radiation with chromatin. Chromatin is modeled as a 30-nm-diameter solenoidal fiber comprised of 20 turns of nucleosomes, 6 nucleosomes per turn. Charged-particle tracks are modeled by partitioning the energy deposition between primary track core, resulting from glancing collisions with 100 eV or less per event, and delta rays due to knock-on collisions involving energy transfers >100 eV. A Monte Carlo simulation incorporates damages due to the following molecular mechanisms: (1) ionization of water molecules leading to the formation of OH, H, eaq, etc.; (2) OH attack on sugar molecules leading to strand breaks: (3) OH attack on bases; (4) direct ionization of the sugar molecules leading to strand breaks; (5) direct ionization of the bases. Our calculations predict significant clustering of damage both locally, over regions up to 40 bp and over regions extending to several kilobase pairs. A characteristic feature of the regional damage predicted by our model is the production of short fragments of DNA associated with multiple nearby strand breaks. The shapes of the spectra of DNA fragment lengths depend on the symmetries or approximate symmetries of the chromatin structure. Such fragments have subsequently been detected experimentally and are reported in an accompanying paper (B. Rydberg, Radiat, Res. 145, 200-209, 1996) after exposure to both high- and low-LET radiation. The overall measured yields agree well quantitatively with the theoretical predictions. Our theoretical results predict the existence of a strong peak at about 85 bp, which represents the revolution period about the nucleosome. Other peaks at multiples of about 1,000 bp correspond to the periodicity of the particular solenoid model of chromatin used in these calculations. Theoretical results in combination with experimental data on fragmentation spectra may help determine the consensus or average structure of the chromatin fibers in mammalian DNA.
Non-NASA Center↗
Theoretical and experimental internal flow characteristics of a 13.97-centimeter-diameter inlet at STOL takeoff and approach conditions
The theoretical and experimental internal flow characteristics of a 13.97-cm-diam inlet with centerbody retracted and extended are presented at STOL takeoff and approach operating conditions. The theoretical results were obtained from incompressible potential flow corrected for compressibility and boundary layer. Comparisons between theoretical internal surface static-pressure distributions and experimental data are presented for free-stream velocities of 0, 24, 32, and 45 m/sec for a range of inlet incidence angles from 0 to 50 deg. Surface static-pressure distributions are illustrated at circumferential locations of 0, 60, 120, and 180 deg. Surface Mach number distributions from the stagnation point to the diffuser exit are presented along with turbulent boundary-layer shape factors. In general, good agreement was found between the theoretical and experimental surface static pressure distributions.
Albers, J. A.↗
Theoretical study of the AlO blue-green (B2Sigma + - X2Sigma +) band system
Two independent, extensive theoretical calculations are reported for the relative band strengths of the AlO (B2Sigma + - X2Sigma +) blue-green system and for the radiative lifetimes of the lowest few vibrational levels of the B2Sigma(+) state. The theoretical lifetimes, which include a small (less than -.5 percent) contribution from bound-bound transitions into the A2Pi state, are in excellent agreement with laser fluorescence studies. The theoretical lifetimes increase monotonically and very slowly with increasing vibrational quantum number. The relative band strengths for the blue-green system derived from the two theoretical calculations are in excellent agreement, but differ systematically from the relative band strengths of Linton and Nicholls (1969). The present results suggest that their self-absorption corrections are not large enough, resulting in relative intensities that are too large, especially for the weak bands with r centroids less than 1.5 A.
Partridge, H.↗
Comparison of experimental surface pressures with theoretical predictions on twin two-dimensional convergent-divergent nozzles
A three-dimensional subsonic aerodynamic panel code (VSAERO) was used to predict the effects of upper and lower external nozzle flap geometry on the external afterbody/nozzle pressure coefficient distributions and external nozzle drag of nonaxisymmetric convergent-divergent exhaust nozzles having parallel external sidewalls installed on a generic twin-engine high performance aircraft model. Nozzle static pressure coefficient distributions along the upper and lower surfaces near the model centerline and near the outer edges (corner) of the two surfaces were calculated, and nozzle drag was predicted using these surface pressure distributions. A comparison between the theoretical predictions and experimental wind tunnel data is made to evaluate the utility of the code in calculating the flow about these types of non-axisymmetric afterbody configurations. For free-stream Mach numbers of 0.60 and 0.90, the conditions where the flows were attached on the boattails yielded the best comparison between the theoretical predictions and the experimental data. For the Boattail terminal angles of greater than 15 deg., the experimental data for M = 0.60 and 0.90 indicated areas of separated flow, so the theoretical predictions failed to match the experimental data. Even though calculations of regions of separated flows are within the capabilities of the theoretical method, acceptable solutions were not obtained.
Carlson, J. R.↗
Consensus theoretic classification methods
Consensus theory is adopted as a means of classifying geographic data from multiple sources. The foundations and usefulness of different consensus theoretic methods are discussed in conjunction with pattern recognition. Weight selections for different data sources are considered and modeling of non-Gaussian data is investigated. The application of consensus theory in pattern recognition is tested on two data sets: 1) multisource remote sensing and geographic data and 2) very-high-dimensional remote sensing data. The results obtained using consensus theoretic methods are found to compare favorably with those obtained using well-known pattern recognition methods. The consensus theoretic methods can be applied in cases where the Gaussian maximum likelihood method cannot. Also, the consensus theoretic methods are computationally less demanding than the Gaussian maximum likelihood method and provide a means for weighting data sources differently.
Benediktsson, Jon A.↗
Theoretical span loading and moments of tapered wings produced by aileron deflection
The effect of tapered ailerons on linearly tapered wings is theoretically determined. Four different aileron spans are considered for each of three wing aspect ratios and each of four wing taper ratios. The change in lift on one half of the wing, the rolling moment, the additional induced drag, and the yawing moment, due to aileron deflection, are represented by non dimensional coefficients. Similar coefficients are given for the damping and yawing moments, the additional drag, and the change in lift, due to rolling. It was found possible to effect a fairly close agreement between the theoretical and experimental rolling moments by introducing into the theoretical expression for the rolling moment an effective change in angle of attack obtained from an analysis of flap data. The theoretical curves show that the highly tapered wing with long ailerons has a lower ratio of yawing to rolling moment and a lower additional induced drag than wings with less taper.
Pearson, H A↗
A theoretical and numerical study of polarimetric scattering and emission from random rough surfaces with anisotropic directional spectrum
In this paper, theoretical and numerical results of the polarimetric scattering and emission from random rough surfaces with anisotropic directional spectrum are presented for the remote sensing of ocean and soil surfaces. The polarimetric scattered field for rough dielectric surfaces is derived to the second order by the small perturbation method (SPM). It is found that the second-order scattered field is coherent in nature, and its coefficients for different polarizations present the lowest-order corrections to the Fresnel reflection coefficients of the surfaces. In addition, the cross-polarized (HV and VH) components of the coherent fields are reciprocal and not zero for surfaces with anisotropic directional spectrum when the azimuth angle of the incident direction is not aligned with the symmetry directions of surfaces. In order to verify the energy conservation condition of the theoretical results, which is important if the theory is to be applied to the passive polarimetry of rough surfaces, a Monte Carlo simulation is performed to numerically calculate the polarimetric reflectivities of one-dimensional random rough surfaces which are generated with a prescribed power-law spectrum in the spectral domain and transformed to the spatial domain by the FFT. The surfaces simulated by this approach are periodic with the period corresponding to the low-wavenumber cutoff. To calculate the scattering from periodic dielectric surfaces, the authors present a new numerical technique which applies the Floquet theorem to reduce the problem to one period and does not require the evaluation of one-dimensional periodic Green's function used in the conventional method of moment formulation. Once the scattering coefficients are obtained, the polarimetric Stokes vectors for the emission from the random surfaces are then calculated according to the Kirchhoff's law and are illustrated as functions of relative azimuth observation and row directions. The second-order SPM is also reduced to this one-dimensional case, and theoretical results for all four Stokes parameters are in excellent agreement with the numerical results obtained from the Monte Carlo simulation. Moreover, the second order coherent fields are found to be necessary for the theoretical evaluation of the third and fourth Stokes parameters. Without that, the reflectivities of random rough surfaces are significantly over-estimated, and the signs of the third and the fourth Stokes parameters are found to be incorrect, if calculated by using the first-order incoherent fields alone.
Yueh, S. H.↗
Theoretical studies of spectroscopic problems of importance for atmospheric radiation measurements
Many of the instruments used to deduce the physical parameters of the Earth's atmosphere necessary for climate studies or for pollution monitoring (for instance, temperature versus pressure or number densities of trace molecules) rely on the existence of accurate spectroscopic data and an understanding of the physical processes responsible for the absorption or emission of radiation. During the summer, research was either continued or begun on three distinct problems: (1) an improved theoretical framework for the calculation of the far-wing absorption of allowed spectral lines; (2) a refinement of the calculation of the collision-induced fundamental spectrum of N2; and (3) an investigation of possible line-mixing effects in the fundamental spectrum of CH4. Progress in these three areas is summarized below. During the past few years, we have developed a theoretical framework for the calculation of the absorption of radiation by the far wings of spectral lines. Such absorption due to water vapor plays a crucial role in the greenhouse effect as well as limiting the retrieval of temperature profiles from satellite data. Several improvements in the theory have been made and the results are being prepared for publication. Last year we published results for the theoretical calculation of the absorption of radiation due to the dipoles induced during binary collisions of N2 molecules using independently measured molecular parameters; the results were in reasonable agreement with experimental data. However, recent measurements have revealed new fine structure that has been attributed to line-mixing effects. We do not think that this is correct, rather that the structure results from short-range anisotropic dipoles. We are in the process of including this refinement in our theoretical calculation in order to compare with the new experimental data. Subtle changes in the spectra of CH4 measured by researchers at Langley have also been attributed to line-mixing effects. By analyzing the same spectral lines we have attempted to verify or rule out possible line-mixing mechanisms. Due to the complexity and richness of the spectrum of this highly symmetric molecule, as well as the small magnitude of the effects, a detailed first-principle calculation of the mixing is a difficult problem. Before such a program is undertaken it is important to glean as much information as possible concerning the possible mechanisms by a systematic analysis of the existing data.
Tipping, Richard H.↗
Theoretical models of polar-cap convection under the influence of a northward interplanetary magnetic field
The unexpected patterns of high-latitude auroral luminosity and ionospheric convection that are observed when the interplanetary magnetic field (IMF) has a northward orientation have inspired a variety of theoretical interpretations. The existing models, all referring to steady-state conditions, can be classified according to the topology of the polar magnetic field lines and of the polar-cap convection streamlines. The classes of model include: (1) a closed magnetosphere model, (2) a conventional open model with a distorted, but topologically unchanged, polar-cap boundary, (3) a conventional open model with distorted, but topologically unchanged, polar-cap convection cells, (4) a modified open model with 'lobe convection cells' contained wholly on open magnetic-field lines, and (5) a modified open model with a bifurcated polar cap. The third and fourth types require significant regions of sunward flow on open polar-cap field lines, a concept that presents serious theoretical difficulties. The other three types appear equally viable from a theoretical point of view, and the comparison against observations is an ongoing enterprise. Outstanding theoretical questions include (a) how do observed structures in the polar ionosphere map along magnetic field lines into the magnetosphere?, (b) what is the mechanism that drives the observed sunward convection at highest latitudes on the day side?, and (c) what role does time dependence play in the observed phenomena?
Hill, T. W.↗
Experimental and Theoretical Study of a Rectangular Wing in a Vortical Wake at Low Speed
A systematic study has been made, experimentally and theoretically, of the effects of a vortical wake on the aerodynamic characteristics of a rectangular wing at subsonic speed. The vortex generator and wing were mounted on a reflection plane to avoid body-wing interference. Vortex position, relative to the wing, was varied both in the spanwise direction and normal to the wing. Angle of attack of the wing was varied from -40 to +60. Both chordwise and spanwise pressure distributions were obtained with the wing in uniform and vortical flow fields. Stream surveys were made to determine the flow characteristics in the vortical wake. The vortex-induced lift was calculated by several theoretical methods including strip theory, reverse-flow theory, and reverse-flow theory including a finite vortex core. In addition, the Prandtl lifting-line theory and the Weissinger theory were used to calculate the spanwise distribution of vortex-induced loads. With reverse-flow theory, predictions of the interference lift were generally good, and with Weissinger's theory the agreement between the theoretical spanwise variation of induced load and the experimental variation was good. Results of the stream survey show that the vortex generated by a lifting surface of rectangular plan form tends to trail back streamwise from the tip and does not approach the theoretical location, or centroid of circulation, given by theory. This discrepancy introduced errors in the prediction of vortex interference, especially when the vortex core passed immediately outboard of the wing tip. The wake produced by the vortex generator in these tests was not fully rolled up into a circular vortex, and so lacked symmetry in the vertical direction of the transverse plane. It was found that the direction of circulation affected the induced loads on the wing either when the wing was at angle of attack or when the vortex was some distance away from the plane of the wing.
Smith, Willard G.↗
Magnetic Reconnection: Theoretical and Observational Perspectives: Preface
Magnetic reconnection is a fundamental plasma-physical process by which energy stored in a magnetic field is converted, often explosively, into heat and the kinetic energy of the charged particles that constitute the plasma. It occurs in a variety of astrophysical settings, ranging from the solar corona to pulsar magnetospheres and winds, as well as in laboratory fusion experiments, where it is responsible for sawtooth crashes. First proposed by R.G. Giovanelli in the late I 940s as the mechanism responsible for solar flares, magnetic reconnection was invoked at the beginning of the space age to explain not just solar flares but also the transfer of energy, mass, and momentum from the solar wind to Earth's magnetosphere and the subsequent storage and release of the transferred energy in the magnetotai\. During the half century or so that has followed the seminal theoretical works by J.W. Dungey, P.A. Sweet, E.N. Parker, and H.E. Petschek, in-situ measurements by Earth-orbiting satellites and remote-sensing observations of the solar corona have provided a growing body of evidence for the occurrence of reconnection at the Sun, in the solar wind, and in the near-Earth space environment. The last thirty years have also seen the development of laboratory reconnection experiments at a number of institutions. In parallel with the efforts of experimentalists in both space and laboratory plasma physics, theorists have investigated, analytically and with the help of increasingly powerful MHD, hybrid, and kinetic numerical simulations, the structure of the diffusion region, the factors controlling the rate, onset, and cessation of reconnection, and the detailed physics that enables the demagnetization of the ions and electrons and the topological reconfiguration of the magnetic field. Moreover, the scope of theoretical reconnection studies has been extended well beyond solar system and laboratory plasmas to include more exotic astrophysical plasma systems whose strong (10(exp 14)-10(exp 15) G) magnetic fields require that models of reconnection in these systems incorporate quantum electrodynamical, special relativistic, and radiative effects. The papers collected in this topical issue of Space Science Reviews cover different aspects of recent theoretical and observational work on magnetic reconnection in solar and space physics, astrophysics, and laboratory plasma physics. They derive from presentations given at a workshop on magnetic reconnection held in the Yosemite National Park, February 8-12,2010. The intent of the workshop was to stimulate, through a combination of tutorial talks, shorter focused talks, and extensive informal discussions, an interdisciplinary dialogue among members of the different research communities working on the problem of magnetic reconnection. One of the motivating considerations for holding the workshop was its relevance to NASA's Magnetospheric Multiscale (MMS) mission, scheduled for launch in 2014. The four identically instrumented MMS spacecraft are designed to study reconnect ion in Earth's magnetosphere and, specifically, to probe the electron diffusion region in order to determine the microphysical processes that enable the change in the topology of the magnetic field. Building on the achievements of the multi spacecraft Cluster and THEMIS missions, MMS will use the magnetosphere as an astrophysical plasma laboratory in which to test, through in-situ measurement of the plasma, energetic particles, and electric and magnetic fields, various models and theories that have emerged during the past twenty years, a period of extraordinarily productive theoretical and observational work.
Lewis, W. S.↗
Comparison of Experimental and Theoretical Zero-Lift Wave-Drag Results for Various Wing-Body-Tail Combinations at Mach Numbers up to 1.9
Comparisons are made of experimental and theoretical zero-lift wave drag for several nose shapes, wing-body combinations, and models of current airplanes at Mach numbers up to 1.0. The experimental data were obtained from tests in the Ames 6- by6-foot supersonic wind tunnel and at the NACA Wallops Island facility. The theoretical drag was found by use of linear theory utilizing model area distributions. The agreement between theoretical and experimental zero-lift wave-drag coefficients was generally very good, especially for a fuselage or for fuselage-wing combinations that were vertically symmetrical. For other models that had rapid changes in body shape and/or were not vertically symmetrical, the agreement of theory with experiment ranged from fair to poor, depending on the severity of the change in shape.
DRAG COEFFICIENT↗
A theoretical and experimental investigation of the hypersonic turbulent boundary layer subject to normal and longitudinal pressure gradients and cross flow along a windward plane of symmetry.
A theoretical and experimental investigation for the hypersonic turbulent boundary layer undergoing both normal and longitudinal pressure gradients and cross flow along the plane of symmetry on the windward side of a body of revolution is presented. The purpose of this investigation is to provide a method for calculating boundary layers that occur on the centerline of symmetry of an inlet. The three-dimensional compressible integral equations are written along the symmetry plane and integrated numerically, and the effect of the cross flow on the behavior of the boundary layer is also studied. The experiments were performed at Mach number 6 and Reynolds number of 44,000,000/ft for the axisymmetric case and for the case with cross flow. The velocity profiles and the boundary layer parameters agree relatively well with theoretical values with and without cross flow effects. The presence of the cross flow alters significantly the value of the profiles. Total temperature-velocity correlations deviate from the linear Crocco distribution. Heat transfer rates agree with theoretical values and values obtained by the flat plate reference enthalpy method. Cross flow influence on the heat transfer rates is of minor relevance.
Zakkay, V.↗