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About: Freestream is a(n) research topic. Over the lifetime, 3428 publication(s) have been published within this topic receiving 56147 citation(s).

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28 Dec 2000
TL;DR: In this article, the authors present an approach to the Viscous Initial Value Problem with the objective of finding the optimal growth rate and the optimal response to the initial value problem.
Abstract: 1 Introduction and General Results.- 1.1 Introduction.- 1.2 Nonlinear Disturbance Equations.- 1.3 Definition of Stability and Critical Reynolds Numbers.- 1.3.1 Definition of Stability.- 1.3.2 Critical Reynolds Numbers.- 1.3.3 Spatial Evolution of Disturbances.- 1.4 The Reynolds-Orr Equation.- 1.4.1 Derivation of the Reynolds-Orr Equation.- 1.4.2 The Need for Linear Growth Mechanisms.- I Temporal Stability of Parallel Shear Flows.- 2 Linear Inviscid Analysis.- 2.1 Inviscid Linear Stability Equations.- 2.2 Modal Solutions.- 2.2.1 General Results.- 2.2.2 Dispersive Effects and Wave Packets.- 2.3 Initial Value Problem.- 2.3.1 The Inviscid Initial Value Problem.- 2.3.2 Laplace Transform Solution.- 2.3.3 Solutions to the Normal Vorticity Equation.- 2.3.4 Example: Couette Flow.- 2.3.5 Localized Disturbances.- 3 Eigensolutions to the Viscous Problem.- 3.1 Viscous Linear Stability Equations.- 3.1.1 The Velocity-Vorticity Formulation.- 3.1.2 The Orr-Sommerfeld and Squire Equations.- 3.1.3 Squire's Transformation and Squire's Theorem.- 3.1.4 Vector Modes.- 3.1.5 Pipe Flow.- 3.2 Spectra and Eigenfunctions.- 3.2.1 Discrete Spectrum.- 3.2.2 Neutral Curves.- 3.2.3 Continuous Spectrum.- 3.2.4 Asymptotic Results.- 3.3 Further Results on Spectra and Eigenfunctions.- 3.3.1 Adjoint Problem and Bi-Orthogonality Condition.- 3.3.2 Sensitivity of Eigenvalues.- 3.3.3 Pseudo-Eigenvalues.- 3.3.4 Bounds on Eigenvalues.- 3.3.5 Dispersive Effects and Wave Packets.- 4 The Viscous Initial Value Problem.- 4.1 The Viscous Initial Value Problem.- 4.1.1 Motivation.- 4.1.2 Derivation of the Disturbance Equations.- 4.1.3 Disturbance Measure.- 4.2 The Forced Squire Equation and Transient Growth.- 4.2.1 Eigenfunction Expansion.- 4.2.2 Blasius Boundary Layer Flow.- 4.3 The Complete Solution to the Initial Value Problem.- 4.3.1 Continuous Formulation.- 4.3.2 Discrete Formulation.- 4.4 Optimal Growth.- 4.4.1 The Matrix Exponential.- 4.4.2 Maximum Amplification.- 4.4.3 Optimal Disturbances.- 4.4.4 Reynolds Number Dependence of Optimal Growth.- 4.5 Optimal Response and Optimal Growth Rate.- 4.5.1 The Forced Problem and the Resolvent.- 4.5.2 Maximum Growth Rate.- 4.5.3 Response to Stochastic Excitation.- 4.6 Estimates of Growth.- 4.6.1 Bounds on Matrix Exponential.- 4.6.2 Conditions for No Growth.- 4.7 Localized Disturbances.- 4.7.1 Choice of Initial Disturbances.- 4.7.2 Examples.- 4.7.3 Asymptotic Behavior.- 5 Nonlinear Stability.- 5.1 Motivation.- 5.1.1 Introduction.- 5.1.2 A Model Problem.- 5.2 Nonlinear Initial Value Problem.- 5.2.1 The Velocity-Vorticity Equations.- 5.3 Weakly Nonlinear Expansion.- 5.3.1 Multiple-Scale Analysis.- 5.3.2 The Landau Equation.- 5.4 Three-Wave Interactions.- 5.4.1 Resonance Conditions.- 5.4.2 Derivation of a Dynamical System.- 5.4.3 Triad Interactions.- 5.5 Solutions to the Nonlinear Initial Value Problem.- 5.5.1 Formal Solutions to the Nonlinear Initial Value Problem.- 5.5.2 Weakly Nonlinear Solutions and the Center Manifold.- 5.5.3 Nonlinear Equilibrium States.- 5.5.4 Numerical Solutions for Localized Disturbances.- 5.6 Energy Theory.- 5.6.1 The Energy Stability Problem.- 5.6.2 Additional Constraints.- II Stability of Complex Flows and Transition.- 6 Temporal Stability of Complex Flows.- 6.1 Effect of Pressure Gradient and Crossflow.- 6.1.1 Falkner-Skan (FS) Boundary Layers.- 6.1.2 Falkner-Skan-Cooke (FSC) Boundary layers.- 6.2 Effect of Rotation and Curvature.- 6.2.1 Curved Channel Flow.- 6.2.2 Rotating Channel Flow.- 6.2.3 Combined Effect of Curvature and Rotation.- 6.3 Effect of Surface Tension.- 6.3.1 Water Table Flow.- 6.3.2 Energy and the Choice of Norm.- 6.3.3 Results.- 6.4 Stability of Unsteady Flow.- 6.4.1 Oscillatory Flow.- 6.4.2 Arbitrary Time Dependence.- 6.5 Effect of Compressibility.- 6.5.1 The Compressible Initial Value Problem.- 6.5.2 Inviscid Instabilities and Rayleigh's Criterion.- 6.5.3 Viscous Instability.- 6.5.4 Nonmodal Growth.- 7 Growth of Disturbances in Space.- 7.1 Spatial Eigenvalue Analysis.- 7.1.1 Introduction.- 7.1.2 Spatial Spectra.- 7.1.3 Gaster's Transformation.- 7.1.4 Harmonic Point Source.- 7.2 Absolute Instability.- 7.2.1 The Concept of Absolute Instability.- 7.2.2 Briggs' Method.- 7.2.3 The Cusp Map.- 7.2.4 Stability of a Two-Dimensional Wake.- 7.2.5 Stability of Rotating Disk Flow.- 7.3 Spatial Initial Value Problem.- 7.3.1 Primitive Variable Formulation.- 7.3.2 Solution of the Spatial Initial Value Problem.- 7.3.3 The Vibrating Ribbon Problem.- 7.4 Nonparallel Effects.- 7.4.1 Asymptotic Methods.- 7.4.2 Parabolic Equations for Steady Disturbances.- 7.4.3 Parabolized Stability Equations (PSE).- 7.4.4 Spatial Optimal Disturbances.- 7.4.5 Global Instability.- 7.5 Nonlinear Effects.- 7.5.1 Nonlinear Wave Interactions.- 7.5.2 Nonlinear Parabolized Stability Equations.- 7.5.3 Examples.- 7.6 Disturbance Environment and Receptivity.- 7.6.1 Introduction.- 7.6.2 Nonlocalized and Localized Receptivity.- 7.6.3 An Adjoint Approach to Receptivity.- 7.6.4 Receptivity Using Parabolic Evolution Equations.- 8 Secondary Instability.- 8.1 Introduction.- 8.2 Secondary Instability of Two-Dimensional Waves.- 8.2.1 Derivation of the Equations.- 8.2.2 Numerical Results.- 8.2.3 Elliptical Instability.- 8.3 Secondary Instability of Vortices and Streaks.- 8.3.1 Governing Equations.- 8.3.2 Examples of Secondary Instability of Streaks and Vortices.- 8.4 Eckhaus Instability.- 8.4.1 Secondary Instability of Parallel Flows.- 8.4.2 Parabolic Equations for Spatial Eckhaus Instability.- 9 Transition to Turbulence.- 9.1 Transition Scenarios and Thresholds.- 9.1.1 Introduction.- 9.1.2 Three Transition Scenarios.- 9.1.3 The Most Likely Transition Scenario.- 9.1.4 Conclusions.- 9.2 Breakdown of Two-Dimensional Waves.- 9.2.1 The Zero Pressure Gradient Boundary Layer.- 9.2.2 Breakdown of Mixing Layers.- 9.3 Streak Breakdown.- 9.3.1 Streaks Forced by Blowing or Suction.- 9.3.2 Freestream Turbulence.- 9.4 Oblique Transition.- 9.4.1 Experiments and Simulations in Blasius Flow.- 9.4.2 Transition in a Separation Bubble.- 9.4.3 Compressible Oblique Transition.- 9.5 Transition of Vortex-Dominated Flows.- 9.5.1 Transition in Flows with Curvature.- 9.5.2 Direct Numerical Simulations of Secondary Instability of Crossflow Vortices.- 9.5.3 Experimental Investigations of Breakdown of Cross-flow Vortices.- 9.6 Breakdown of Localized Disturbances.- 9.6.1 Experimental Results for Boundary Layers.- 9.6.2 Direct Numerical Simulations in Boundary Layers.- 9.7 Transition Modeling.- 9.7.1 Low-Dimensional Models of Subcritical Transition.- 9.7.2 Traditional Transition Prediction Models.- 9.7.3 Transition Prediction Models Based on Nonmodal Growth.- 9.7.4 Nonlinear Transition Modeling.- III Appendix.- A Numerical Issues and Computer Programs.- A.1 Global versus Local Methods.- A.2 Runge-Kutta Methods.- A.3 Chebyshev Expansions.- A.4 Infinite Domain and Continuous Spectrum.- A.5 Chebyshev Discretization of the Orr-Sommerfeld Equation.- A.6 MATLAB Codes for Hydrodynamic Stability Calculations.- A.7 Eigenvalues of Parallel Shear Flows.- B Resonances and Degeneracies.- B.1 Resonances and Degeneracies.- B.2 Orr-Sommerfeld-Squire Resonance.- C Adjoint of the Linearized Boundary Layer Equation.- C.1 Adjoint of the Linearized Boundary Layer Equation.- D Selected Problems on Part I.

2,182 citations

01 Oct 1992
TL;DR: In this article, two new versions of the k-omega two-equation turbulence model are presented, the baseline model and the Shear-Stress Transport model, which is based on the BSL model, but has the additional ability to account for the transport of the principal shear stress in adverse pressure gradient boundary layers.
Abstract: Two new versions of the k-omega two-equation turbulence model will be presented. The new Baseline (BSL) model is designed to give results similar to those of the original k-omega model of Wilcox, but without its strong dependency on arbitrary freestream values. The BSL model is identical to the Wilcox model in the inner 50 percent of the boundary-layer but changes gradually to the high Reynolds number Jones-Launder k-epsilon model (in a k-omega formulation) towards the boundary-layer edge. The new model is also virtually identical to the Jones-Lauder model for free shear layers. The second version of the model is called Shear-Stress Transport (SST) model. It is based on the BSL model, but has the additional ability to account for the transport of the principal shear stress in adverse pressure gradient boundary-layers. The model is based on Bradshaw's assumption that the principal shear stress is proportional to the turbulent kinetic energy, which is introduced into the definition of the eddy-viscosity. Both models are tested for a large number of different flowfields. The results of the BSL model are similar to those of the original k-omega model, but without the undesirable freestream dependency. The predictions of the SST model are also independent of the freestream values and show excellent agreement with experimental data for adverse pressure gradient boundary-layer flows.

1,679 citations

Journal ArticleDOI
Chul Park1
TL;DR: In this paper, a two-temperatur e chemical-kinet ic model for air is assessed by comparing theoretical results with existing experimental data obtained in shock tubes, ballistic ranges, and flight experiments.
Abstract: A two-temperatur e chemical-kinet ic model for air is assessed by comparing theoretical results with existing experimental data obtained in shock tubes, ballistic ranges, and flight experiments. In the model, one temperature (T) is assumed to characterize the heavy-particle translational and molecular rotational energies, and another temperature (Tv) the molecular vibrational, electron translational, and electronic excitation energies. The theoretical results for nonequilibrium flow in shock tubes are obtained using the computer code STRAP (shock-tube radiation program) and for flow along the stagnation streamline in the shock layer over spherical bodies using the newly developed code SPRAP (stagnation-point radiation program). Substantial agreement is shown between the theoretical and experimental results for relaxation times and radiative heat fluxes. At very high temperatures, the spectral calculations need further improvement. The present agreement provides strong evidence that the two-temperature model characterizes principal features of nonequilibriu m airflow. New theoretical results using the model are presented for the radiative heat fluxes at the stagnation point of 6 m radius sphere, representing an aeroassisted orbital transfer vehicle, over a range of freestream conditions. Assumptions, approximations, and limitations of the model are discussed. Nomenclature = average molecular speed ^/$kT/nm, cm s ~ ! = pre-exponential factor in reaction rate coefficient, cm3mole~ 1 s~ * - average vibrational energy per particle, erg = average vibrational energy per particle under equilibrium, erg = reaction energy, erg

631 citations

Journal ArticleDOI
TL;DR: In this article, the authors defined the upper surface lift coefficient of an airfoil chord and defined the freestream conditions at the leading edge of the chord line, and the ratio of specific heats.
Abstract: Nomenclature c = airfoil chord CL = lift coefficient = L/!/2pV00c CLu = upper-surface lift coefficient Cp = pressure coefficient = (p -p^)/ Ap Vx 2 Mx = freestream Mach number p = static pressure Re^ = freestream Reynolds number based on airfoil chord = V^clv sp = location of leading-edge stagnation point V^ — freestream velocity v local velocity on airfoil surface x = distance along chord line F = circulation about the airfoil 7 = ratio of specific heats v = kinematic viscosity p = density () oo = freestream conditions () t e = conditions at the airfoil trailing edge

489 citations

Journal ArticleDOI
TL;DR: The boundary-layer receptivity to external acoustic and vortical disturbances is reviewed in this article. But, the authors do not consider the effects of external acoustic or vortic disturbances on the boundary layer.
Abstract: The current understanding of boundary-layer receptivity to external acoustic and vortical disturbances is reviewed. Recent advances in theoretical modeling, numerical simulations, and experiments are discussed. It is shown that aspects of the theory have been validated and that the mechanisms by which freestream disturbances provide the initial conditions for unstable waves are better understood. Challenges remain, however, particularly with respect to freestream turbulence

479 citations

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