# Showing papers in "AIAA Journal in 1975"

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TL;DR: In this article, an incomplete set of free-boundary normal modes of vibration, augmented with a low-frequency account for the contribution of neglected (residual) modes is described.

Abstract: The new method described in this paper employs an incomplete set of free-boundary normal modes of vibration, augmented with a low-frequency account for the contribution of neglected (residual) modes. The "residual effects" improve the accuracy of forced dynamic response in a manner which is related to the benefit of the mode-acceleration method. The new method adds residual inertial and dissipative effects to the residual flexibility introduced by MacNeal. All effects are derived from the solution of a special statics problem, followed by removal of the contributions of the retained modes. A structural component can then be represented in a stiffness-matrix form for various applications, one of which is modal synthesis. Numerical results of modal analysis for a cantilevered rod show the new method to yield superior accuracy to several other methods (including those of Hurty, Bamford, and MacNeal). All parameters for the new representation can be derived from test; this is not true for most other methods. Required are the free-boundary normal modes and the dynamic flexibility matrix vs frequency for the boundary points. Consequently, any desired mix of analytically derived and experimentally derived parameters can be employed.

576 citations

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TL;DR: In this paper, the amplitude ratio of constant-frequency disturbances as a function of Reynolds number for insulated and cooled-wall flat-plate boundary layers between Mach numbers 1.3 and 5.8 is calculated.

Abstract: Compressible linear stability theory is first reviewed and then used to calculate the amplitude ratio of constant-frequency disturbances as a function of Reynolds number for insulated and cooled-wall flat-plate boundary layers between Mach numbers 1.3 and 5.8. These results are used to examine the consequences of using a fixed disturbance amplitude of the most unstable frequency as a transition criterion. The effect of the freestream Mach number M1 on the transition of insulated-wall boundary layers is calculated using two different assumptions concerning the initial boundary-layer disturbance amplitude A0. It is found that the shape of the transition Reynolds number Ret vs MI curve observed in wind tunnels can be closely duplicated. As a second example, the effect of wall cooling at MI = 3.0 is calculated. A much faster increase of Re, with cooling is obtained than is observed experimentally. However, when A0 is determined from the forced response of the boundary layer to irradiated sound and from the measured freestream power spectrum, a rise in Re, similar to what is observed is obtained for a certain amplitude criterion.

515 citations

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TL;DR: In this paper, hot-wire anemometry is used to study the origin and growth of "natural" fluctuations in zero pressure-gradient boundary layers for several Mach numbers between 1.6 and 8.5.

Abstract: Hot-wire anemometry is used to study the origin and growth of "natural" fluctuations in zero pressure-gradient boundary layers for several Mach numbers between 1.6 and 8.5. The importance to transition of certain physical mechanisms is examined through comparison of the fluctuation growth with the sound-forcing and stability theories of Mack. Flow fluctuations of substantial amplitude were observed within the laminar layer ahead of stations where instability amplification is expected to be important. These fluctuations were found to be cross-correlated with the sound field for the higher supersonic speeds, but not for the lower ones. The fluctuation growth rates in the unstable Reynolds number range ahead of the nonlinearity region were in reasonably close agreement with the theory for Mach 4.5; the agreement for Mach 2.2 and 8.5 was qualitative. The second mode of instability was predominant at Mach 8.5.

391 citations

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Virginia Tech

^{1}TL;DR: A critical review of the state of the art regarding methods of determining the transmission and attenuation parameters and the effect on these parameters of (1) acoustic properties of liners, (2) the mean velocity, including uniform and shear profiles and nonparallel flow, axial and transverse temperature gradients, slowly and abruptly varying cross sections, and finite-amplitude waves and nonlinear duct liners is presented in this paper.

Abstract: Noise generated in aircraft engines is usually suppressed by acoustically treating the engine ducts. The optimization of this treatment requires an understanding of the transmission and attenuation of the acoustic waves. A critical review is presented of the state of the art regarding methods of determining the transmission and attenuation parameters and the effect on these parameters of (1) acoustic properties of liners, (2) the mean velocity, including uniform and shear profiles and nonparallel flow, (3) axial and transverse temperature gradients, (4) slowly and abruptly varying cross sections, and (5) finite-amplitude waves and nonlinear duct liners.

228 citations

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TL;DR: In this paper, a general formulation for steady and oscillatory, subsonic and supersonic, potential linearized aerodynamic flows around complex configurations is presented, where the surface is divided into small quadrilateral elements which are approximated with hyperboloidal surfaces.

Abstract: A general formulation for steady and oscillatory, subsonic and supersonic, potential linearized aerodynamic flows around complex configurations is presented. A linear integral equation relating the unknown potential on the surface of the body to the known downwash is used. The formulation is applied to the analysis of flowfields around wings and wing-body combinations. The surface is divided into small quadrilateral elements which are approximated with hyperboloidal surfaces. The potential is assumed to be constant within each element. This yields a set of linear algebraic equations. The coefficients are evaluated analytically. Numerical results for steady and oscillatory, subsonic and supersonic flows indicate that the method, is not only more general and flexible than other available methods, but is also fast, accurate, and in excellent agreement with existing results.

214 citations

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TL;DR: In this paper, the oscillatory character of the flow was achieved without the use of moving parts by incorporating a fluidic feedback loop into the nozzle design, and the thrust efficiencies approached 90% and the half-width spreading rates exceeded that of the slot nozzle by a factor of more than three.

Abstract: A nozzle development program was undertaken to produce a time-dependent flow at the nozzle exit. The oscillatory character of the flow was achieved without the use of moving parts by incorporating a fluidic feedback loop into the nozzle design. The nozzle thrust efficiencies approached 90% and the half-width spreading rates attained exceeded that of the slot nozzle by a factor of more than three.

194 citations

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TL;DR: In this paper, the large amplitude vibrations of a thin-walled cylindrical shell are analyzed using the Donnell's shallow-shell equations and a perturbation method is applied to reduce the nonlinear partial differential equations into a system of linear PDEs.

Abstract: The large amplitude vibrations of a thin-walled cylindrical shell are analyzed using the Donnell's shallow-shell equations. A perturbation method is applied to reduce the nonlinear partial differential equations into a system of linear partial differential equations. The simply-supported boundary condition and the circumferential periodicity condition are satisfied. The resulting solution indicates that in addition to the fundamental modes, the response contains asymmetric modes as well as axisymmetric modes with the frequency twice that of the fundamental modes. In the previous investigations in which the Galerkins procedure was applied, only the additional axisymrnetric modes were assumed.
Vibrations involving a single driven mode response are investigated. The results indicate that the nonlinearity is either softening or hardening depending on the mode. The vibrations involving both a driven mode and a companion mode are also investigated. The region where the companion mode participates in the vibration is obtained and the effects due to the participation of the companion mode are studied.
An experimental investigation is also conducted. The
results are generally in agreement with the theory. "Non-stationary4 response is detected at some frequencies for large amplitude response where the amplitude drifts from one value to another. Various nonlinear phenomena are observed and quantitative comparisons with the theoretical results are made.

177 citations

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TL;DR: In this paper, a simple model is proposed in which the shock wave is convected from its mean position by velocity fluctuations in the turbulent boundary layer, and the displacement of the shock is assumed limited by a linear restoring mechanism.

Abstract: Pressure fluctuations due to the interaction of a shock wave with a turbulent boundary layer were investigated. A simple model is proposed in which the shock wave is convected from its mean position by velocity fluctuations in the turbulent boundary layer. Displacement of the shock is assumed limited by a linear restoring mechanism. Predictions of peak root mean square pressure fluctuation and spectral density are in excellent agreement with available experimental data.

155 citations

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TL;DR: Garnet, H. and Armen, H., Evaluation of Numerical Time Integration Methods as Applied to Elastic-Plastic Dynamic Problems Involving Wave Propagation, Rept. RE-475, March 1974, Research Dept., Grumman Aircraft Corp., Bethpage, N.Y. as mentioned in this paper.

Abstract: 2 Garnet, H. and Armen, H., Evaluation of Numerical Time Integration Methods as Applied to Elastic-Plastic Dynamic Problems Involving Wave Propagation, Rept. RE-475, March 1974, Research Dept., Grumman Aircraft Corp., Bethpage, N.Y. 3 Stoodley, G. R. and Ball, D. J., Mathematical Background of Two Numerical Integration Techniques for Ordinary Differential Equations, Memo. RM-192, Oct. 1961, Research Dept, Grumman Aircraft Corp., Bethpage, N.Y. 4 Mantus, M., Lerner, E., and Elkins, W., "Landing Dynamics of the Lunar Excursion Module (Method of Analysis)," Rept. LED-5206A, Revised April 10, 1967, Grumman Aircraft Corp., Bethpage, N.Y. 5 Lerner, E. and Mantus, M., "Dynamics of Unsymmetric Landing," Rept. ADR 02-10-10-62-1, Jan. 1963, Grumman Aircraft Corp, Bethpage, N.Y. 6 Donnell, L. H., "Longitudinal Wave Transmission and Impact," Transactions of the ASME, Vol, 52, 1930, pp. 153-167. 7 DeJuhasz, K. J., "Graphical Analysis of Impact of Bars Stressed Above the Elastic Range," Journal of the Franklin Institute, Vol. 248, No. 2, Aug. 1949, pp. 113-142. 8 Davids, N. and Kumar, S., "A Contour Method for One Dimensional Pulse Propagation in Elastic-Plastic Materials," Proceedings of the Third U.S. National Congress of Applied Mechanics, Brown University, Providence, R.I., 1958, pp. 502-512. 9 Garnet, H. and Armen, H., One Dimensional Elastic-Plastic Wave Propagation and Boundary Reflections, Memo, Grumman Research Department, Bethpage, N.Y. (in preparation).

146 citations

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TL;DR: In this paper, it was shown that Hamilton's law permits the direct analytical solution to nonstationary, initial value systems in the mechanics of solids without any knowledge or use of the theory of differential equations associated therewith.

Abstract: The law of varying action enunciated by Hamilton in 1834-1835 permits the direct analytical solution of the problems of mechanics, both stationary and nonstationary, without consideration of force equilibrium and the theory of differential equations associated therewith. It has not been possible to obtain direct analytical solutions to nonstationary systems through the use of energy theory, which has been limited for 140 years to the principle of least action and to Hamilton's principle. It is shown here that Hamilton's law permits the direct analytical solution to nonstationary, initial value systems in the mechanics of solids without any knowledge or use of the theory of differential equations. Solutions are demonstrated for nonconservative, nonstationary particle motion, both linear and nonlinear.

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TL;DR: In this paper, two numerical methods are presented for computing the derivatives of eigenvalues and eigenvectors which do not require complete solution of the eigenvalue problem if only a few derivatives are sought.

Abstract: Two numerical methods are presented for computing the derivatives of eigenvalues and eigenvectors which do not require complete solution of the eigenvalue problem if only a few derivatives are sought. The 'iterative' method may be used to find the first derivative of one or all of the eigenvectors together with the second derivative of their eigenvalues in a self-adjoint system. If the left- and right-hand eigenvectors are known, the first derivative of the eigenvector corresponding to the largest eigenvalue and the second derivative of the largest eigenvalue may be obtained for a nonself-adjoint system. The 'algebraic' method may be used to find all orders of the derivatives, provided they exist, without requiring the left-hand eigenvectors.

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BBN Technologies

^{1}TL;DR: An evanescent-wa ve formulation relates sound radiated from subsonic turbulent flow at the edge of a semi-infinite rigid surface to a wavevector-frequency spectral density P(K,u>) of hydrodynamic pressure as mentioned in this paper.

Abstract: An evanescent-wa ve formulation relates sound radiated from subsonic turbulent flow at the edge of a semiinfinite rigid surface to a wavevector-frequency spectral density P(K,u>) of hydrodynamic pressure This has been used to obtain the frequency spectra of nearfield pressure in the surface and of farfield radiated pressure and the cross-spectrum between them A model differing from those used previously is suggested for P(K,u>) to fit the frequency dependence of nearfield (and radiated) pressure spectra measured in jet-flow experiments and is interpreted to indicate dominance by the mean-shear source term Results are applied to a recent experiment where a jet streamed off a flat surface With model parameters determined mainly from nearfield surface pressure spectra, the predicted radiated spectrum agrees well with that measured The measured crosscorrelations between nearfield and radiated pressure plotted vs edge distance from the nearfield point at different frequencies roughly coalesce when normalized in accord with a predicted universal form and agree adequately with the result of the model Significant validation of the method and of the proposed characterization of hydrodynamic pressure is thus obtained for the given flow configuration Extension to two-sided flows is discussed

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TL;DR: Birnbaum, M. M. and Salomon, P. M., "Strapdown Star Tracker for Space Vehicle Attitude Control," Journal of Spacecraft and Rockets, Vol. 5, No. 2, Oct. 1968, pp. 1188-1192.

Abstract: 1 Nash, J. M., "On the Use of a Simple Stellar Sighter to Determine Booster Navigation Error Parameters," Ph.D. thesis, March 1974, Engineering Systems Department, University of California, Los Angeles, Calif. 2 Meditch, J. S., Stochastic Optimal Linear Estimation and Control, McGraw-Hill, New York, 1969. 3 Birnbaum, M. M. and Salomon, P. M., "Strapdown Star Tracker for Space Vehicle Attitude Control," Journal of Spacecraft and Rockets, Vol. 5, Oct. 1968, pp. 1188-1192. 4 Goldstein, H., Classical Mechanics, Addison-Wesley, Reading, Mass., 1950.

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TL;DR: In this paper, the effect of compressibility on the mixing layer was investigated at Mach number 2, and the difference between free and wall-bounded mixing layers was discussed. And the development of turbulence structure of mixing layer with increasing Reynolds number was also investigated.

Abstract: The effect of compressibility on the mixing layer was investigated at Mach number 2.47. Pitot pressure, static pressure, and hot-wire surveys were conducted to investigate the mean flow and the fluctuation quantities. Similarities between supersonic and incompressible mixing layers were observed in normalized velocity profile, normalized power spectral density distribution, and convection velocity distribution. Spreading rate, normalized shear stress, and velocity fluctuation were found to be appreciably smaller than the respective incompressible results; e.g., the momentum thickness growth rates are 0.0073 and 0.035 for supersonic and incompressible flows, respectively. The difference between free and wall-bounded mixing layers is discussed. Development of turbulence structure of mixing layer with increasing Reynolds number was also investigated.

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TL;DR: In this paper, the Taylor-Gortler vortices observed in a nozzle wall boundary layer were used to predict the limits of quiet performance for a proposed 20-in. quiet tunnel.

Abstract: High noise levels in conventional supersonic and hypersonic wind tunnels prevent further advances in transition research. Recent data confirm previous results that transition is dominated by tunnel noise when the rms pressure intensities exceed about 1%. High facility noise levels also dominate fluctuating pressure loads under fully turbulent boundary layers. Recent data on the power spectra of surface pressures indicate that the basic structure of turbulent boundary layers may be modified by high facility noise levels. Experimental data for current techniques to control and reduce noise levels in supersonic and hypersonic wind tunnels by laminarization of nozzle wall boundary layers and by noise radiation shields are presented. These results and possible effects of Taylor-Gortler vortices observed in a nozzle wall boundary layer are used to predict the limits of quiet performance for a proposed 20-in. quiet tunnel.

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TL;DR: In this article, a finite-element analysis was used to predict crack-closure and crack-opening stresses during specified histories of cyclic loading, and this analysis was subsequently used to study the crackclosure behavior under constant amplitude and simple block-program loading.

Abstract: Fatigue cracks have been experimentally shown to close at positive stresses during constant-amplitude load cycling. The crack-closure phenomenon is caused by residual plastic deformations remaining in the wake of an advancing crack tip. This paper is concerned with the development and application of a two-dimensional finiteelement analysis to predict crack-closure and crack-opening stresses during specified histories of cyclic loading. An existing finite-element computer program which accounts for elastic-plastic material behavior under cyclic loading was modified to account for changing boundary conditions—crack growth and intermittent contact of crack surfaces. This program was subsequently used to study the crack-closure behavior under constantamplitude and simple block-program loading. a [B]

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TL;DR: In this article, the importance of unsteady effects on laminar boundary layers was found to diminish rapidly with increasing longitudinal pressure gradients, whereas turbulent separation on airfoils was significantly affected by oscillatory motion when the incidence approached the stall angle.

Abstract: Incompressible laminar and turbulent flows over flat plates and airfoils have been investigated numerically and experimentally in unsteady flow conditions. Important differences were found between laminar and turbulent flat plate flows over a wide range of oscillation frequencies. Also, the importance of unsteady effects on laminar boundary layers was found to diminish rapidly with increasing longitudinal pressure gradients, whereas turbulent separation on airfoils was significantly affected by oscillatory motion when the incidence approached the stall angle. The calculated hysteresis in turbulent separation followed in a qualitative sense the well-known trends of dynamic stall delay and reattachment. However, the numerical analysis failed to indicate some of the important features of dynamic stall observed in the present experiment and in previous studies.

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TL;DR: Theoretical and experimental studies on microbuckling compression failure of fiber-reinforced unidirectional composites subjected to compression loads parallel to the fiber direction are presented in this article.

Abstract: Theoretical and experimental studies are presented on microbuckling compression failure of fiber-reinforced unidirectional composites subjected to compression loads parallel to the fiber direction. The approximate microbuckling equation is derived by the energy method. Results predicted from this equation are compared with test data and good agreement is found, indicating that for certain combinations of constituents, microbuckling is a valid failure mode. The influence of the following parameters on microbuckling is investigated theoretically and experimentally: fiber volume fraction, fiber shape, fiber size, properties of fibers and resins, fiber-end configuration, and specimen geometry. Other failure modes for composites subjected to compression loading are also briefly discussed.

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TL;DR: In this paper, the growth rate of the boundary layer thickness over the convex side is almost halved and the skin friction coefficient falls to about 0.9 of the value expected on a plane surface.

Abstract: Measurements are reported for turbulent boundary-layer growth in a prolonged bend where the additional rates of strain produced by streamline curvature influence the turbulent development. The growth rate of the boundary-layer thickness over the convex side is almost halved and the skin friction coefficient falls to about 0.9 of the value expected on a plane surface. The mixing rate on the concave side is increased to about 1.1 times the plane surface value, and the customary evidence of longitudinal rolls appears. These measurements are the first since those of Schmidbauer's (1936) to provide a test of existing curvature correction formulas for curvatures typical of airfoils and turbomachinery without the complications of compressibility. Results have been compared against calculation techniques proposed by Bradshaw (1973), with good agreement.

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TL;DR: In this article, the influence of blade mistiming on the vibratory stress levels of turbine and compressor blades is investigated, and it is shown that a large number of resonances may occur over a frequency band, the width of which is nearly 20% of the mean blade frequency.

Abstract: This analysis is aimed at determining the influence of blade mistiming on the vibratory stress levels of turbine and compressor blades A frequency response analysis for a given rotor configuration shows that a large number of resonances may occur over a frequency band, the width of which is nearly 20% of the mean blade frequency The resonant amplitudes are a function of blade frequency and location on the rotor, and the amount of damping present in the system A parametric study is carried out to evaluate the response levels due to engine order excitation, aerodynamic and mechanical damping, and blade frequency deviation The resulting mode shapes and frequencies are in good agreement with the experimental findings reported earlier in the literature

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TL;DR: In this paper, the structure of the flowfields formed about the muzzle of a small caliber rifle during the firing were measured using a time-resolved, spark shadow-graph technique. But the results were limited.

Abstract: The structure of the flowfields formed about the muzzle of a small caliber rifle during the firing are measured using a time-resolved, spark shadow-graph technique. The initial flow from the muzzle occurs as tube gases are forced out ahead of the projectile. The gas is air and the exit properties are Ve =945 m/sec, Me = 1.48 and Pel POO = 15. A second flowfield forms upon separation of the projectile which releases the propellant gases. After an initial, in-bore expansion, the propellant gas muzzle properties are Ve=\29S m/sec, Afe = 1.0, and Pe/Poo =600. While the exit properties are different, the flowfields develop in a similar manner. In the axial or downrange direction, strong coupling between the jet and blast fields is observed; however, along the lateral boundaries, the coupling is very weak with the jet structure remaining invariant once established. Motion of observable discontinuities along the axis of symmetry is shown to qualitatively agree with variable energy blast wave theory. At late times, the air blast and jet flows are shown to uncouple and decay independently.

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TL;DR: In this article, the nonlinear collapse behavior of long cylindrical shell structures subject to a bending load only or combined bending and uniform normal pressure loads is studied using the STAGS computer code.

Abstract: The nonlinear collapse behavior of long cylindrical shell structures subject to a bending load only or combined bending and uniform normal pressure loads is studied using the STAGS computer code. Two modes of nonlinear collapse are investigated to determine maximum strength. One mode of collapse is described by circumferential flattening of the cylinder cross section, while the other mode is represented by axial wrinkling in the region of maximum compression. Results compare favorably with available published data for cylinders loaded by pure bending, and results are presented for combined loads which have not been previously reported. The collapse loads obtained in this study show that current design criteria are conservative except for a narrow range of length-to-radius ratios and pressures.

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TL;DR: In this paper, an explicit finite-difference method with time splitting is used to solve the time-dependent equations for compressible turbulent flow, and a nonorthogonal computational mesh of arbitrary configuration facilitates the description of the flow field.

Abstract: A code has been developed for simulating high Reynolds number transonic flow fields of arbitrary configuration. An explicit finite-difference method with time splitting is used to solve the time-dependent equations for compressible turbulent flow. A nonorthogonal computational mesh of arbitrary configuration facilitates the description of the flow field. The code is applied to simulate the flow over an 18 percent thick circular-arc biconvex airfoil at zero angle of attack and free-stream Mach number of 0.775. A simple mixing-length model is used to describe the turbulence and chord Reynolds numbers of 1, 2, 4, and 10 million are considered. The solution describes in sufficient detail both the shock-induced and trailing-edge separation regions, and provides the profile and friction drag.

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TL;DR: In this paper, a modified eddy viscosity model is incorporated into the compressible Navier-Stokes equations to reproduce the response of turbulence to a severe pressure gradient in the flowfield.

Abstract: A modified eddy viscosity model is incorporated into the compressible Navier-Stokes equations. The modification attempts to reproduce the response of turbulence to a severe pressure gradient in the flowfield. This relaxation phenomenon is described by an exponential decay of the unperturbed eddy viscosity coefficient downstream of the perturbation in terms of a prescribed length scale. The system of equations is solved by MacCormack's time-splitting explicit numerical scheme for a series of compression corner configurations. Computations are performed for ramp angles varying from 15 to 25° at a Mach number of 2.96 and a Reynolds number of 10 7. Calculations utilizing the modified eddy viscosity for the interacting turbulent flow compare very well with experimental measurements, particularly in the prediction of the upstream pressure propagation and location of the separation and the reattachment points. Good agreement is also attained between the measured and calculated density profiles in the viscous-inviscid interaction region.

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TL;DR: In this article, a detailed model of the burning rate of an ammonium perchlorate solid composite propellant to pressure and velocity fluctuations is presented, where the authors show that an additive law applies, and a pressure and velocities sensitive erosive component is added to the normal pressure sensitive burning rate.

Abstract: A detailed model is presented which permits one to represent the response of the burning rate of an ammonium perchlorate solid composite propellant to pressure and velocity fluctuations First, the steady regime response of the burning velocity of a propellant exposed to a turbulent boundary layer is described The well-known granular diffusion flame model is employed, with the changes in the transport coefficients taken into account It is shown (and not assumed) that, according to the present model, an additive law applies; a pressure and velocity sensitive erosive component is added to the normal pressure sensitive burning rate By coupling the unsteady behavior of the propellant solid phase to the quasisteady flame zone, represented by the abovementioned model, the linearized response of the propellant to pressure and velocity oscillations is obtained

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TL;DR: In this article, a finite difference solution is developed for the unsteady compressible flow between the Mach disk and the blast wave, assuming spherical symmetry, to obtain a quantitative representation of the inviscid gas dynamics of the blast field.

Abstract: The muzzle blast field generated by a gun-launched high-velocity projectile is characterized by a highly underexpanded supersonic exhaust plume, which terminates at a strong shock (the Mach disk), an expanding front of exhaust gases (the contact surface), and an expanding, nearly spherical outer shock (the blast wave). The present study is directed toward theoretical description of the inviscid gas dynamics of the blast field. The rioted features are discussed in terms of well-establis hed theories for spherical blast waves with variable energy release and for steady underexpanded plumes, from which their interaction can be qualitatively described. To obtain a quantitative representation, a finite difference solution is developed for the unsteady compressible flow between the Mach disk and the blast wave, assuming spherical symmetry. The results obtained are in good agreement with experimental measurements of the motion of the blast wave, the contact surface and Mach disk for a 3200 fps round fired from an M16 rifle. a B C d E