Linearized Compressible-flow Theory for Sonic Flight Speeds
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Heaslet, Max A↗
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New constitutive equation for the volume viscosity in fluids
The traditional volume viscosity, Stokes' hypothesis, and acoustical relaxation are reviewed. The lossy Navier-Stokes Equation is applied to periodic (acoustic) flow, and it is shown that the traditional volume viscosity leads to a result which contradicts that describing acoustical relaxation. It is demonstrated that the addition of a second volume viscosity term to the constitutive equation, to account for pressure relaxation, resolves the conflict, and leads to a direct correspondence between the volume viscosity parameters and the acoustical relaxation parameters. The representation of volume viscosity is formulated for the case of multiple relaxations, as occur in air. Finally, an application of the new constitutive equation to a simple convective compressible flow, namely a linearly accelerating flow, demonstrates the impact of volume viscosity upon the flow and the physical conditions for which it is important.
Zuckerwar, Allan J.↗
Exploiting Dense Sensitivity Matrices in Linear Optimal Power Flow.
Abstract not provided.
Eldridge, Brent↗
Gust response analysis for cascades operating in nonuniform mean flows
The linearized unsteady aerodynamic response of a cascade of airfoils subjected to entropic, vortical, and acoustic gusts is analyzed. Field equations for the first-order unsteady perturbation flow are obtained by linearizing the full time-dependent mass, momentum, and energy conservation equations about a nonlinear, isentropic, and irrotational mean or steady flow. A splitting technique is then used to decompose the unsteady velocity field into irrotational and rotational parts leading to field equations for the unsteady entropy, rotational velocity, and irrotational velocity fluctuations that are coupled only sequentially. The entropic and rotational velocity fluctuations can be described in terms of the mean-flow drift and stream functions which can be computed numerically. The irrotational unsteady velocity is described by an inhomogeneous linearized potential equation which contains a source term that depends on the rotational velocity field. This equation is solved via a finite difference technique. Results are presented to indicate the status of the numerical solution procedure and to demonstrate the impact of blade geometry and mean blade loading on the aerodynamic response of cascades to vortical gust excitations. The analysis described leads to very efficient predictions of cascade unsteady aerodynamic phenomena making it useful for turbomachinery aeroelastic and aeroacoustic design applications.
Hall, Kenneth C.↗
Gust response analysis for cascades operating in nonuniform mean flows
The linearized unsteady aerodynamic response of a cascade of airfoils subjected to entropic, vortical, and acoustic gusts is analyzed. Field equations for the first-order unsteady perturbation flow are obtained by linearizing the full time-dependent mass, momentum, and energy conservation equations about a nonlinear, isentropic, and irrotational mean or steady flow. A splitting technique is then used to decompose the unsteady velocity field into irrotational and rotational parts leading to field equations for the unsteady entropy, rotational velocity, and irrotational velocity fluctuations that are coupled only sequentially. The entropic and rotational velocity fluctuations can be described in terms of the mean-flow drift and stream functions which can be computed numerically. The irrotational unsteady velocity is described by an inhomogeneous linearized potential equation which contains a source term that depends on the rotational velocity field. This equation is solved via a finite difference technique. Results are presented to indicate the status of the numerical solution procedure and to demonstrate the impact of blade geometry and mean blade loading on the aerodynamic response of cascades to vortical gust excitations. The analysis described leads to very efficient predictions of cascade unsteady aerodynamics phenomena making it useful for turbomachinery aeroelastic and aeroacoustic design applications.
Hall, Kenneth C.↗
A model for transonic plasma flow
A linear, two-dimensional model of a transonic plasma flow in equilibrium is constructed and given an explicit solution in the form of a complex Laplace integral. The solution indicates that the transonic state can be solved as an elliptic boundary value problem, as is done in the numerical code FLOW [Guazzotto et al., Phys. Plasmas 11, 604 (2004)]. Moreover, the presence of a hyperbolic region does not necessarily imply the presence of a discontinuity or any other singularity of the solution.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Film stability in a vertical rotating tube with a core-gas flow.
The linear hydrodynamic stability of a thin-liquid layer flowing along the inside wall of a vertical tube rotating about its axis in the presence of a core-gas flow is examined. The stability problem is formulated under the conditions that the liquid film is thin, the density and viscosity ratios of gas to liquid are small and the relative (axial) pressure gradient in the gas is of the same order as gravity. The resulting eigenvalue problem is first solved by a perturbation method appropriate to axisymmetric long-wave disturbances. The damped nature (to within the thin-film and other approximations made) of the nonaxisymmetric and short-wave disturbances is noted. In view of the limitations on a truncated perturbation solution when the disturbance wavenumber is not small, an initial value method using digital computer is presented. Stability characteristics of neutral, growing, and damped modes are presented showing the influences of rotation, surface tension, and the core-gas flow. Energy balance in a neutral mode is also illustrated.
Sarma, G. S. R.↗
Mixer Analysis of Nacelle/Nozzle Flow
Flow over idealized nozzle computed. Analysis and computer program calculate flow over idealized mixer nozzle. Nozzle idealized by unwrapping it so planform lies in z=O plane. Linearized compresible flow used to calculate flow and mixer shape given loading on mixer. End goal to achieve maximum amount of mixing downstream of mixer while retaining reasonable shape for mixer. Because analysis assumes linearized flow, calculation of effects of deep lobe penetration cannot be made using this program.
Barber, T. J.↗
Subcritical transition to turbulence in plane channel flows
A linear three dimensional mechanism for the transition of plane Poiseuille flows to turbulence is presented which provides good agreement with experimental observations. The mechanism is based on the evolution of states within a band of quasi-equilibria which slowly approach the stable upper branch solutions for the evolution of flow energy but which are strongly unstable to infinitesimal three-dimensional disturbances. Numerical simulation has shown that if two-dimensional flow persists long enough for the three-dimensional perturbations to attain finite amplitude, the resulting three dimensional flow quickly develops a turbulent character with nonperiodic behavior, and thus transition can be predicted from knowledge of the initial two- and three-dimensional energies and time scales. The mechanism predicts transition to turbulence at Reynolds numbers greater than 1000, as observed in experiments, and implies higher threshold three-dimensional energies in plane Couette flow.
Orszag, S. A.↗
Correspondence flows for wings in linearized potential fields at subsonic and supersonic speeds
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THEORIES - WINGS↗
Hydrokinetic power conversion using Flow Induced Vibrations with nonlinear (adaptive piecewise-linear) springs
Not Available
Sun, Hai (ORCID:0000000188552288)↗
Nonparallel stability of three-dimensional flows
The linear stability of three-dimensional incompressible, isothermal, nonparallel boundary-layer flows has been investigated. The method of multiple scales is used to derive the partial-differential equations that describe the spatial modulations of the amplitude, phase and wavenumber of a disturbance. Group velocities are used to determine the disturbance growth direction. The envelope method is used to calculate the logarithmic amplitude growth rate N. The theory is applied to the flows over a swept-back tapered wing with boundary-layer suction. Results of such analysis for the X-21 wing are discussed. It is found that the nonparallel effects for this wing is substantial.
Padhye, A. R.↗
Advanced surface paneling method for subsonic and supersonic flow
Numerical results illustrating the capabilities of an advanced aerodynamic surface paneling method are presented. The method is applicable to both subsonic and supersonic flow, as represented by linearized potential flow theory. The method is based on linearly varying sources and quadratically varying doublets which are distributed over flat or curved panels. These panels are applied to the true surface geometry of arbitrarily shaped three dimensional aerodynamic configurations.
Erickson, L. L.↗
The similarity rules for second-order subsonic and supersonic flow
The similarity rules for linearized compressible flow theory (Gothert's rule and its supersonic counterpart) are extended to second order. It is shown that any second-order subsonic flow can be related to "nearly incompressible" flow past the same body, which can be calculated by the Janzen-Rayleigh method.
Van Dyke, Milton D↗
Linear permeability evolution of expanding conduits due to feedback between flow and fast phase change: Linear Permeability Evolution of Conduit
Conduits are ubiquitous and critical pathways for many fluids relevant for geophysical processes such as magma, water, and gases. Predicting flow through conduits is challenging when the conduit geometry coevolves with the flow. We theoretically show that the permeability (k) of a conduit whose walls are eroding due to fast phase change increases linearly with time because of a self-reinforcing mechanism. This simple result is surprising given complex feedbacks between flow, transport, and phase change. The theory is congruent with previous experimental observations of fracture dissolution in calcite. Supporting computational fracture dissolution experiments showed that k only slightly increases until the dissolution front reaches the narrowest conduit constriction, after which the linear evolution of k manifests. Finally, the theory holds across multiple scales and a broad range of Peclet and Damkohler numbers and thus advances the prediction of dynamic mass fluxes through expanding conduits in various geologic and environmental settings
58 GEOSCIENCES↗
Prediction of Undsteady Flows in Turbomachinery Using the Linearized Euler Equations on Deforming Grids
A linearized Euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and blade motion is presented. The model accounts for blade loading, blade geometry, shock motion, and wake motion. Assuming that the unsteadiness in the flow is small relative to the nonlinear mean solution, the unsteady Euler equations can be linearized about the mean flow. This yields a set of linear variable coefficient equations that describe the small amplitude harmonic motion of the fluid. These linear equations are then discretized on a computational grid and solved using standard numerical techniques. For transonic flows, however, one must use a linear discretization which is a conservative linearization of the non-linear discretized Euler equations to ensure that shock impulse loads are accurately captured. Other important features of this analysis include a continuously deforming grid which eliminates extrapolation errors and hence, increases accuracy, and a new numerically exact, nonreflecting far-field boundary condition treatment based on an eigenanalysis of the discretized equations. Computational results are presented which demonstrate the computational accuracy and efficiency of the method and demonstrate the effectiveness of the deforming grid, far-field nonreflecting boundary conditions, and shock capturing techniques. A comparison of the present unsteady flow predictions to other numerical, semi-analytical, and experimental methods shows excellent agreement. In addition, the linearized Euler method presented requires one or two orders-of-magnitude less computational time than traditional time marching techniques making the present method a viable design tool for aeroelastic analyses.
Clark, William S.↗
A finite difference method for the solution of the transonic flow around harmonically oscillating wings
A finite difference method for the solution of the transonic flow about a harmonically oscillating wing is presented. The partial differential equation for the unsteady transonic flow was linearized by dividing the flow into separate steady and unsteady perturbation velocity potentials and by assuming small amplitudes of harmonic oscillation. The resulting linear differential equation is of mixed type, being elliptic or hyperbolic whereever the steady flow equation is elliptic or hyperbolic. Central differences were used for all derivatives except at supersonic points where backward differencing was used for the streamwise direction. Detailed formulas and procedures are described in sufficient detail for programming on high speed computers. To test the method, the problem of the oscillating flap on a NACA 64A006 airfoil was programmed. The numerical procedure was found to be stable and convergent even in regions of local supersonic flow with shocks.
Ehlers, E. F.↗
Calculation of unsteady flows in turbomachinery using the linearized Euler equations
A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).
Hall, Kenneth C.↗