# Showing papers in "AIAA Journal in 1978"

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TL;DR: An implicit finite-difference scheme is developed for the numerical solution of the compressible Navier-Stokes equations in conservation- law form and, although a three-time-lev el scheme, requires only two time levels of data storage.

Abstract: An implicit finite-difference scheme is developed for the numerical solution of the compressible Navier-Stokes equations in conservation- law form. The algorithm is second-order- time accurate, noniterative, and spatially factored. In order to obtain an efficient factored algorithm, the spatial cross derivatives are evaluated explicitly. However, the algorithm is unconditional ly stable and, although a three-time-lev el scheme, requires only two time levels of data storage. The algorithm is constructed in a "delta" form (i.e., increments of the conserved variables and fluxes) that provides a direct derivation of the scheme and leads to an efficient computational algorithm. In addition, the delta form has the advantageous property of a steady state (if one exists) independent of the size of the time step. Numerical results are presented for a two-dimensiona l shock boundary-layer interaction problem.

2,096 citations

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TL;DR: In this paper, an automatic grid generation program is employed, and because an implicit finite-difference algorithm for the flow equations is used, time steps are not severely limited when grid points are finely distributed.

Abstract: Finite-difference procedures are used to solve either the Euler equations or the "thin-layer" Navier-Stokes equations subject to arbitrary boundary conditions. An automatic grid generation program is employed, and because an implicit finite-difference algorithm for the flow equations is used, time steps are not severely limited when grid points are finely distributed. Computational efficiency and compatibility to vectorized computer processors is maintained by use of approximate factorization techniques. Computed results for both inviscid and viscous flow about airfoils are described and compared to viscous known solutions.

691 citations

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621 citations

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403 citations

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TL;DR: The Lagrange function for the stiffness matrix weighted norm of the errors between the given and the optimal stiffness matrix unity matrix is defined in this paper, where the error is defined as the difference between the error between the desired stiffness matrix and the given stiffness matrix.

Abstract: Nomenclature Lagrange function for the flexibility matrix weighted norm of the errors between the given and the optimal flexibility matrix Lagrange function for the stiffness matrix weighted norm of the errors between the given and the optimal stiffness matrix unity matrix given stiffness matrix mass matrix M» //element of TV //element of N~* Nq general-coordinates vector measured mode shape /th measured_mode shape normalized 7} transpose of [ • ] = optimal flexibility matrix = (/ element of W orthogonal mode shape matrix = (/ element of X optimal stiffness matrix -ij element of Y = matrices of Lagrange multipliers = ij element of 0y and 0W , respectively = matrix of Lagrange multipliers = given flexibility matrix = matrices of Lagrange multipliers = ij element of A^ and A^ , respectively = measured frequency matrix = //element of Q y»(i* w

303 citations

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276 citations

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TL;DR: In this article, mixed formulations are introduced as a means for reducing severe constraints in finite-element derivations for plate bending elements to include transverse shear effect and to be applicable also to thin plates.

Abstract: Mixed formulations are introduced as a means for reducing severe constraints in finite-element derivations. For plate bending elements to include transverse shear effect and to be applicable also to thin plates, the method can reduce the conditions of constraints of zero transverse shear strain energy. For shell elements, the constraints of rigid-body modes can be lessened similarly. Certain mixed formulations have been shown to be equivalent to displacement models with reduced integration scheme. But the present approach provides a general and rational method for the finite-element development. Illustrative examples include plate, circular arch, and shell elements.

229 citations

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TL;DR: In this article, the indicial method is used for the computation of unsteady transonic force and moment coefficients for use in flutter analyses. But it is not suitable for the analysis of aeroelastic systems.

Abstract: The indicial method is investigated for the computation of unsteady transonic force and moment coefficients for use in flutter analyses. This approach has the advantage that solutions for all reduced frequencies for a given mode of motion can be obtained from a single finite-difference flowfield computation. Comparisons of indicial and time-integration computations for oscillating airfoil and flap motions help define limits on the motion amplitude for the applicability of the indicial method to transonic flows. Within these limits, solutions for various motion modes can be superposed to obtain solutions for multiple-degree-of-freedom aeroelastic systems. Also, a simple aeroelastic problem is solved by an alternative approach in which the structural motion and flowfield equations are integrated simultaneously using a time-integration finite-difference procedure.

220 citations

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TL;DR: In this article, an analytical investigation on the influence of bond thickness upon the stress distribution in single-lap adhesive joints is presented. But the results of this study were not included in any of the numerous analytical investigations reviewed.

Abstract: Results of an analytical investigation on the influence of bond thickness upon the stress distribution in singlelap adhesive joints are presented. The present work extends the basic approach for bonded joints, orginally introduced by Goland and Reissner, through use of a more complete shear-strain/displacement equation for the adhesive layer. This refinement was not found to be included in any of the numerous analytical investigations reviewed. As a result of the approach employed, the present work uncovers several interesting phenomena without adding any significant complication to the analysis. Besides modifying some coefficients in the shear stress equations, completely new terms in the differential equation and boundary conditions for bond peel stress are obtained. Sn addition, a variation of shear stress through the bond thickness, no matter how thin it may be, is analytically predicted only by the present theory. This through-the-bond-thickness variation of shear stress identifies two antisymmetrical adherend-bond interface points at which the shear stresses are highest. The growth of joint failures originating from these points agrees with results obtained from actual experiments.

195 citations

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TL;DR: In this paper, a theoretical analysis has been conducted based on the model that positive ions produced by ionization near the wire electrode move toward the plate, introducing the bulk convective motion of neutral molecules as the result of collisions of ions and neutral molecules.

Abstract: The corona wind, with a velocity of several meters per second, is caused by applying high electric tension to bring about corona discharge in gases. In this paper the corona wind is experimentally and theoretically analyzed from an electrohydrod ynamical (EHD) standpoint. Experiments have been performed mainly in nitrogen by a two-dimensional electrode arrangement of a fine wire anode and a plate cathode. The voltage-current characteristics of an electrostatic probe indicate that positive ions predominate in the whole space except in an extremely narrow region close to the wire. A theoretical analysis has been conducted based on the model that positive ions produced by ionization near the wire electrode move toward the plate, introducing the bulk convective motion of neutral molecules as the result of collisions of ions and neutral molecules. The electric potential distribution in the space and pressure distribution on the plate calculated numerically agree well with the experimental data. Consequently, it is made clear that the corona wind is caused by the Coulomb force exerted on ions and collisions of ions and neutral molecules of gas.

195 citations

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TL;DR: The algebraic eddy viscosity model of Cebeci and Smith has been modified to account for wall roughness by incorporating a suggestion of Rotta as discussed by the authors, and the boundary-layer equations are solved, with this model, by the accurate and efficient Keller Box scheme for a wide variety of experimental configurations.

Abstract: The algebraic eddy viscosity model of Cebeci and Smith has been modified to account for wall roughness by incorporating a suggestion of Rotta. The boundary-layer equations are solved, with this model, by the accurate and efficient Keller Box scheme for a wide variety of experimental configurations. These include adverse, zero, and favorable pressure gradients, and roughness elements that approach the upper limits of Rotta's model. Comparison of calculated and measured values of skin friction and integral thickness confirms the applicability of the procedure for all cases presented.

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TL;DR: In this paper, a simple, rational approach is presented for developing continuum models for large repetitive beam and plate-like lattices with arbitrary configurations subjected to static, thermal, and dynamic loadings.

Abstract: A simple, rational approach is presented for developing continuum models for large repetitive beam- and platelike lattices with arbitrary configurations subjected to static, thermal, and dynamic loadings. The continuum models for these structures are shear flexible beams and plates. They account for local effects in the repeating element of the actual structure and are characterized by their thermoelastic strain and kinetic energies, from which the equations of motion and constitutive relations can be derived. The procedure for developing the expressions for thermoelastic strain and kinetic energies of the continuum involves introducing basic assumptions regarding the variation of the temperature, displacement, and strain components in one or two directions (for plate- and beamlike lattices) and obtaining effective thermoelastic and dynamic coefficients of the continuum in terms of material properties and geometry of the original lattice structure. The high accuracy of the continuum models developed is demonstrated by means of numerical examples. AltA2,Ab,Ad

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TL;DR: In this paper, an experimental and computational investigation of the steady and unsteady transonic flowfields about a thick airfoil is described, and an operational computer code for solving the two-dimensional, compressible NavierStokes equations for flow over airfoils was modified to include solid-wall, slip-flow boundary conditions to properly assess the code and help guide the development of improved turbulence models.

Abstract: An experimental and computational investigation of the steady and unsteady transonic flowfields about a thick airfoil is described. An operational computer code for solving the two-dimensional, compressible NavierStokes equations for flow over airfoils was modified to include solid-wall, slip-flow boundary conditions to properly assess the code and help guide the development of improved turbulence models. Steady and unsteady fiowfieids about an 18% thick circular arc airfoil at Mach numbers of 0.720, 0.754, and 0.783 and a chord Reynolds number of 11 x 10 are predicted and compared with experiment. Results from comparisons with experimental pressure and skin-friction distributions show improved agreement when including test-section wall boundaries in the computations. Steady-flow results were in good quantitative agreement with experimental data for flow conditions which result in relatively small regions of separated flow. For flows with larger regions of separated flow, improvements in turbulence modeling are required before good agreement with experiment will be obtained. For the first time, computed results for unsteady turbulent flows with separation caused by a shock wave were obtained which qualitatively reproduce the time-dependent aspects of experiments. Features such as the intensity and reduced frequency of airfoil surface-pressure fluctuations, oscillatory regions of trailing-edge and shock-induced separation, and the Mach number range for unsteady flows were all qualitatively reproduced.

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TL;DR: In this article, the effects of transverse compressional damping in the vibratory response of three-layer elastic-viscoelasticelastic beams are considered both analytically and experimentally in a mechanical impedance format.

Abstract: The effects of transverse compressional damping in the vibratory response of three-layer elastic-viscoelasticelastic beams are considered both analytically and experimentally in a mechanical impedance format. The relative importance of this type of damping is assessed through comparison with the shear damping mechanism inherent in the composite using the Mead and Markus model. Results of this investigation suggest that the effects from transverse compressional damping have a relatively narrow frequency bandwidth dependent on the elastic loss tangent of the damping core and are centered at the compressional (delamination) frequency toc of the composite. Compressional damping is shown to have a minimal effect on the transverse dynamic response of thin three-layer damped beams for frequencies significantly less than coc where a shear damping model provides a more accurate prediction of the composite loss factor. / £ tv /,b EI Pi

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TL;DR: In this article, a system of two-dimensional al nonsteady hydrodynamic and chemical kinetic equations was numerically integrated for an exothermic system and a fixed number of triple shock waves were produced for a fixed combination of mixture model and geometry when the transition period was over.

Abstract: In the present work, a system of two-dimension al nonsteady hydrodynamic and chemical kinetic equations was numerically integrated for an exothermic system. An assumed two-step reaction model simulates an oxyhydrogen mixture. The calculation starts from a plane Chapman-Jouguet detonation as an initial condition. Two-dimensional disturbances are generated by artificially placing nonuniformities ahead of the detonation front. Regardless of the difference in the given initial disturbances, a fixed number of triple shock waves were produced for a fixed combination of mixture model and geometry when the transition period was over. This shows that for a given detonation tube geometry, any exothermic system has its own characteristic multidimensional structure. The obtained number of triple shock waves contained in the detonation front was in agreement with existing experimental observations under the same condition.

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TL;DR: In this article, a mathematical and computational capability has been developed for calculating the effective mechanical properties of three-dimensional periodic truss-like structures, and two models are studied in detail.

Abstract: A mathematical and computational analysis capability has been developed for calculating the effective mechanical properties of three-dimensional periodic truss-like structures. Two models are studied in detail. The first, called the octetruss model, is a three-dimensional extension of a two-dimensional model, and the second is a cubic model. Symmetry considerations are employed as a first step to show that the specific octetruss model has four independent constants and that the cubic model has two. The actual values of these constants are determined by averaging the contributions of each rod element to the overall structure stiffness. The individual rod member contribution to the overall stiffness is obtained by a three-dimensional coordinate transformation. The analysis shows that the effective three-dimensional elastic properties of both models are relatively close to each other.

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TL;DR: In this paper, a model of the plasmadynamics and subsequent energy transfer to the surface by radiation and conduction is constructed to predict the thermal coupling coefficient (coupled energy/laser energy) for pulsed laser irradiation of a metal target.

Abstract: Recent experimental data have indicated that when highly reflective metal targets are irradiated by pulsed lasers in an air environment, a larger fraction of the incident laser energy is coupled into the target when a plasma is ignited above the surface than when plasma formation does not occur. Models of the plasmadynamics and subsequent energy transfer to the surface by radiation and conduction are constructed in order to predict the thermal coupling coefficient (coupled energy/laser energy) for pulsed laser irradiation of a metal target. It is found that the largest fraction of the incident laser energy is coupled into the target when a laser-supported combustion wave is ignited in close proximity to the surface. Energy transfer is via reradiation from the absorbing air plasma. Techniques for obtaining maximum thermal coupling are suggested as a result of the theoretical models. Results are compared with both computer simulations of the plasmadynamics and existing experimental data.

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TL;DR: In this paper, a wide range of geometrical grid parameters and grid set operating conditions were investigated for their effect on ion beam divergence in two-grid accelerator systems, and the results showed that beam divergence depends most strongly on the normalized perveance per hole, grid separation ratio, net-to-total accelerating voltage ratio, and discharge-to total voltage ratio variations.

Abstract: The first comprehensive experimental investigation of two-grid accelerator systems is presented. A wide range of geometrical grid parameters and grid set operating conditions were investigated for their effect on ion beam divergence. Ion beam divergence was found to depend most strongly on normalized perveance per hole, grid separation ratio, net-to-total accelerating voltage ratio, and discharge-to-total accelerating voltage ratio variations. The graphical results contained herein provide guidelines for the design of ion accelerator systems. A general ion beam divergence angle correlation was developed to permit approximate beam divergence estimates, at parametric values other than those tested, of present grid set designs. Although argon was the main test gas used in this study, it is shown that the results are applicable to other propellants as well.

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TL;DR: In this article, a closed-form analytical solution is obtained by using a double application of the Wiener-Hopf technique for predicting the unsteady flow in a supersonic cascade with subsonic axial flow velocity.

Abstract: Linearized theory is used to predict the unsteady flow in a supersonic cascade with subsonic axial flow velocity. A closed-form analytical solution is obtained by using a double application of the Wiener-Hopf technique. Although numerical and semianalytical solutions of this problem have already appeared in the literature, this paper contains the first completely analytical solution. It has been stated in the literature that the blade source should vanish at the infinite duct resonance condition. The present analysis shows that this does not occur. This apparent discrepancy is explained in the paper.

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TL;DR: In this paper, an investigation of the transonic flow over a circular arc airfoil was conducted to obtain basic information for turbulence modeling of shock-induced separated flows and to verify numerical computer codes which are being developed to simulate such flows.

Abstract: An investigation of the transonic flow over a circular arc airfoil was conducted to obtain basic information for turbulence modeling of shock-induced separated flows and to verify numerical computer codes which are being developed to simulate such flows. The investigation included the employment of a laser velocimeter to obtain data concerning the mean velocity, the shear stress, and the turbulent kinetic energy profiles in the flowfield downstream of the airfoil midchord where the flow features are more complex. Depending on the free-stream Mach number, the flowfield developed was either steady with shock-wave-induced separation extending from the foot of the shock wave to beyond the trailing edge or unsteady with a periodic motion also undergoing shock-induced separation. The experimental data were compared with the results of numerical simulations in which a computer code was employed that solved the time-dependent Reynolds' averaged compressible Navier-Stokes equations.

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TL;DR: In this paper, a new numerical scheme based on exponential difference operator concepts combined with Keller's (1968) box scheme approach was proposed to produce a stable second-order accurate finite-difference scheme for convection-diffusion problems arising in boundary layer flows in the presence of massive injection through a porous surface.

Abstract: The paper describes a new numerical scheme based on exponential difference operator concepts combined with Keller's (1968) box scheme approach to produce a stable second-order accurate finite-difference scheme for convection-diffusion problems arising in boundary layer flows in the presence of massive injection through a porous surface. The technique is demonstrated by application to the self-similar boundary layer equations with massive blowing at the surface.

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TL;DR: In this paper, a simple eddy viscosity model is developed, and the interaction of a swept shock wave and a three-dimensional turbulent boundary layer is studied, and good agreement is obtained between the present results and experimental measurements for the case of a wedge with an angle of 6 deg on a flat-plate sidewall.

Abstract: A rapid numerical scheme is used to solve the complete mass-averaged Navier-Stokes equations for supersonic turbulent flow over a three-dimensional compression corner. A simple eddy viscosity model is developed, and the interaction of a swept shock wave and a three-dimensional turbulent boundary layer is studied. Good agreement is obtained between the present results and experimental measurements for the case of a wedge with an angle of 6 deg on a flat-plate sidewall. For the case of a 12-deg wedge angle, the computed results do not show the existence of a peak pressure found experimentally. However, the range of interaction, the plateau pressure, and the peak heat transfer are closely predicted for all cases. The high heat transfer near the axial corner is due to the thinning of the boundary layer and inflow of fresh high-momentum fluid. The heat transfer is relieved through pressure reduction and boundary-layer thickening.

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TL;DR: In this paper, it is shown analytically and experimentally that a transition can occur from a combustion noise-dominant situation to an entropy noisedominant case if the contraction of a terminating nozzle to the combustor is high enough.

Abstract: This paper deals with noise sources which are centra! to the problem of core engine noise in turbopropulsion systems. The sources dealt with are entropy noise and direct combustion noise, as well as a nonpropagating psuedosound which is hydrodynaniic noise. It is shown analytically and experimentally that a transition can occur from a combustion noise-dominant situation to an entropy noise-dominant case if the contraction of a terminating nozzle to the combustor is high enough. In the conibustor tested, entropy noise is the dominant source for propagationai noise if the combustor is choked at the exit. It is also speculated that there might be another unexplored noise source interior of the combustor. Analysis techniques include spectral, cross spectral, correlation, and ordinary and partial coherence analysis. Measurements include exterior and interior fluctuating and mean pressures and temperatures. T has been known for some time that there are at least two probable causes for core noise—entropy or indirect noise and direct combustion noise.! Direct combustion noise is caused by a fluid dilatation caused by a fluctuating heat release. Entropy noise is caused by hot (or cold) spots passing through the pressure gradients of. the turbine assembly. Both noise sources have the same fundamental cause—heat release fluctuations—but they are formed in a different manner. Entropy noise depends upon the heat release history following a fluid element through the combustor, whereas combustion noise depends on the instantaneous aggregate heat release rate fluctuation. The purpose of this program was to isolate the two suspected causes of core noise and determine their relative importance to the core noise problem. It is clear that core noise presents a noise floor in current turbopropulsion systems, but there is controversy concerning the strength of core noise relative to other sources.2'4 It is sufficient to remark here that core noise exists and is measurable. Entropy and combustion noise are not the only possibilities for core noise. Another possibility is vorticity- nozzle interaction nose,5 which is essentially a resistance of a nozzle to pass an axial velocity fluctuation. While sources other than entropy and combustion noise are not directly investigated here, the analysis techniques do reveal whether or not entropy and combustion noise are dominant over other sources. The analysis techniques presented essentially try to relate processes taking place inside a combustor to the noise radiated to the surroundings. One troublesome problem encountered in a prior program6 was the contamination of interior pressure fluctuation measurements by non- propagating psuedosound (hydrodynamic noise). Another purpose of this paper was to eliminate this contaminant as much as possible in order to concentrate on propagationai sound and its causes.

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Virginia Tech

^{1}TL;DR: In this article, the viscous shock-layer equations have been extended to treat blunt three-dimensional bodies at angle of attack, and numerical solutions have been obtained on sphere-cones at angles of attack up to 38 deg.

Abstract: The viscous shock-layer equations have been extended to treat blunt three-dimensional bodies at angle of attack. Numerical solutions have been obtained on sphere-cones at angles of attack up to 38 deg. Comparisons are made with available experimental data, inviscid solutions, and solutions of the parabolized Navier-Stokes equations. The experimental data consisted of heat-transfer distributions, pressure distributions, and drag coefficients in a Mach number range from 10-18, Reynolds numbers of the order 1.3 x 10 4/ft, and a from 0-40 deg. Two cases were compared with the parabolized Navier-Stokes solutions at Mach numbers of 22.77 and 25.81 and altitudes of 180 and 240 kft at angles of attack of 23 and 38 deg, respectively. In general, the shocklayer predictions were in good agreement with the available experimental and numerical data, but the parabolic treatment of the crossflow viscous shock-layer equations prevented solutions on the leeward side of long bodies at large angles of attack. cp C'

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TL;DR: Results indicate that the AF method requires substantially less computer time than SLOR to solve the nonlinear finite-difference matrix equation for the flowfield, and increases in computational efficiency with virtually no increase in computer storage or coding complexity.

Abstract: Implicit appproximate-factorization (AF) algorithms are developed for the solution of steady-state transonic flow problems. The performance of the AF solution method is evaluated relative to that of the standard solution method for transonic flow problems, successive line over-relaxation (SLOR). Both methods are applied to the solution of the nonlinear, two-dimensional transonic small-disturbance equation for flows about representative transonic airfoils. Results indicate that the AF method requires substantially less computer time than SLOR to solve the nonlinear finite-difference matrix equation for the flowfield. This increase in computational efficiency is achieved with virtually no increase in computer storage or coding complexity.

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TL;DR: In this article, the turbulent near-wake of a cylindrical blunt-based body aligned with a uniform freestream was experimentally investigated using an upstream model support system.

Abstract: The turbulent near-wake of a cylindrical blunt-based body aligned with a uniform freestream was experimentally investigated Tests were conducted over the entire subsonic Mach number range in a wind tunnel utilizing an upstream model support system Results indicate that the separation process influences the flow approaching the blunt base for at least 3 model diameters The base pressure coefficient is constant for Mach numbers less than 08, but drops rapidly at near-sonic speeds The size of the near-wake increases with Mach number A similarity expression for the near-wake centerline velocity distribution is developed

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TL;DR: In this paper, the authors studied the effect of vortex drift on the dispersion of two-dimensional trailed vortex pairs within simplified neutral atmospheric backgrounds for three conditions: when the pair is imbedded in a constant turbulent bath (constant dissipation), when the vortex pair is subjected to a mean cross-wind shear, and when it is near the ground.

Abstract: Enhanced dispersion of two-dimensional trailed vortex pairs within simplified neutral atmospheric backgrounds is studied numerically for three conditions: when the pair is imbedded in a constant turbulent bath (constant dissipation); when the pair is subjected to a mean crosswind shear; and when the pair is near the ground. Turbulent transport is modeled using second-order closure turbulent transport theory. The computed results allow several general conclusions to be drawn with regard to the reduction in circulation of the vortex pair and the rolling moment induced on a following aircraft: 1) the rate of decay of a vortex pair increases with increasing background dissipation rate; 2) crosswind shear disperses the vortex whose vorticity is opposite to the background; and 3) the proximity of a ground plane reduces the hazard of the pair by scrubbing. The phenomenon of vortex bounce is explained in terms of secondary vorticity produced at the ground plane. Qualitative comparisons are made with available experimental data, and inferences of these results upon the persistence of aircraft trailing vortices are discussed.

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TL;DR: In this paper, the authors developed a method to determine the acoustic power produced by turbofans as a function of mode cutoff ratio, which is essential for the design of acoustic suppressors in engine ducts.

Abstract: The far-field sound radiation theory for a circular duct was studied for both single-mode and multimodal inputs. The investigation was intended to develop a method to determine the acoustic power produced by turbofans as a function of mode cutoff ratio. This information is essential for the design of acoustic suppressors in engine ducts. With reasonable simplifying assumptions, the single-mode radiation pattern was shown to be reducible to a function of mode cutoff ratio only (modal indices removed). With modal cutoff ratio as the dominant variable, multimodal radiation patterns can be reduced to a simple explicit expression. This approximate expression provides excellent agreement with an exact calculation of the sound radiation pattern using equal acoustic power per mode. Radiation patterns for cases other than equal modal power are presented using the approximate radiation equation. An approximate expression for the duct termination losses as a function of cutoff ratio also is included.