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At least 1,189 records · Page 66
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Nonlinear Instability of a Uni-directional Transversely Sheared Mean Flow

It is well known that the presence of a weak cross flow in an otherwise two-dimensional shear flow results in a spanwise variation in the mean streamwise velocity profile that can lead to an amplification of certain three-dimensional disturbances through a kind of resonant-interaction mechanism (Goldstein and Wundrow 1994). The spatial evolution of an initially linear, finite-growth-rate, instability wave in such a spanwise-varying shear flow is considered, The base flow, which is governed by the three-dimensional parabolized Navier-Stokes equations, is initiated by imposing a spanwise- periodic cross-flow velocity on an otherwise two-dimensional shear flow at some fixed streamwise location. The resulting mean-flow distortion initially grows with increasing streamwise distance, reaches a maximum and eventually decays through the action of viscosity. This decay, which coincides with the viscous spread of of the shear layer, means that the local growth rate of the instability wave will eventually decrease as the wave propagates downstream. Nonlinear effects can then become important within a thin spanwise-modulated critical layer once the local instability-wave amplitude and growth rate become sufficiently large and small, respectively. The amplitude equation that describes this stage of evolution is shown to be a generalization of the one obtained by Goldstein and Choi (1989) who considered the related problem of the interaction of two oblique modes in a two-dimensional shear layer.

Wundrow, David W.↗
NASA NTRS2004

Adjoint Formulation for an Embedded-Boundary Cartesian Method

Many problems in aerodynamic design can be characterized by smooth and convex objective functions. This motivates the use of gradient-based algorithms, particularly for problems with a large number of design variables, to efficiently determine optimal shapes and configurations that maximize aerodynamic performance. Accurate and efficient computation of the gradient, however, remains a challenging task. In optimization problems where the number of design variables dominates the number of objectives and flow- dependent constraints, the cost of gradient computations can be significantly reduced by the use of the adjoint method. The problem of aerodynamic optimization using the adjoint method has been analyzed and validated for both structured and unstructured grids. The method has been applied to design problems governed by the potential, Euler, and Navier-Stokes equations and can be subdivided into the continuous and discrete formulations. Giles and Pierce provide a detailed review of both approaches. Most implementations rely on grid-perturbation or mapping procedures during the gradient computation that explicitly couple changes in the surface shape to the volume grid. The solution of the adjoint equation is usually accomplished using the same scheme that solves the governing flow equations. Examples of such code reuse include multistage Runge-Kutta schemes coupled with multigrid, approximate-factorization, line-implicit Gauss-Seidel, and also preconditioned GMRES. The development of the adjoint method for aerodynamic optimization problems on Cartesian grids has been limited. In contrast to implementations on structured and unstructured grids, Cartesian grid methods decouple the surface discretization from the volume grid. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin e t al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation.

Nemec, Marian↗
NASA NTRS2002

Constitutive properties of hypertrophied myocardium: cellular contribution to changes in myocardial stiffness

Recent studies have suggested that pressure overload hypertrophy (POH) alters the viscoelastic properties of individual cardiocytes when studied in isolation. However, whether these changes in cardiocyte properties contribute causally to changes in the material properties of the cardiac muscle as a whole is unknown. Accordingly, a selective, isolated, acute change in cardiocyte constitutive properties was imposed in an in vitro system capable of measuring the resultant effect on the material properties of the composite cardiac muscle. POH caused an increase in both myocardial elastic stiffness, from 20.5 +/- 1.3 to 28.4 +/- 1.8, and viscous damping, from 15.2 +/- 1.1 to 19.8 +/- 1.5 s (normal vs. POH, P < 0.05), respectively. Recent studies have shown that cardiocyte constitutive properties could be acutely altered by depolymerizing the microtubules with colchicine. Colchicine caused a significant decrease in the viscous damping in POH muscles (19.8 +/- 1.5 s at baseline vs. 14.7 +/- 1.3 s after colchicine, P < 0.05). Therefore, myocardial material properties can be altered by selectively changing the constitutive properties of one element within this muscle tissue, the cardiocyte. Changes in the constitutive properties of the cardiocytes themselves contribute to the abnormalities in myocardial stiffness and viscosity that develop during POH.

Non-NASA Center↗
NASA NTRS1997

Implicit/Multigrid Algorithms for Incompressible Turbulent Flows on Unstructured Grids

An implicit code for computing inviscid and viscous incompressible flows on unstructured grids is described. The foundation of the code is a backward Euler time discretization for which the linear system is approximately solved at each time step with either a point implicit method or a preconditioned Generalized Minimal Residual (GMRES) technique. For the GMRES calculations, several techniques are investigated for forming the matrix-vector product. Convergence acceleration is achieved through a multigrid scheme that uses non-nested coarse grids that are generated using a technique described in the present paper. Convergence characteristics are investigated and results are compared with an exact solution for the inviscid flow over a four-element airfoil. Viscous results, which are compared with experimental data, include the turbulent flow over a NACA 4412 airfoil, a three-element airfoil for which Mach number effects are investigated, and three-dimensional flow over a wing with a partial-span flap.

Anderson, W. Kyle↗
NASA NTRS2004

Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method

Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented an effective optimization framework that incorporates a direct-CAD interface. In this work, we enhance the capabilities of this framework with efficient gradient computations using the discrete adjoint method. We present details of the adjoint numerical implementation, which reuses the domain decomposition, multigrid, and time-marching schemes of the flow solver. Furthermore, we explain and demonstrate the use of CAD in conjunction with the Cartesian adjoint approach. The final paper will contain a number of complex geometry, industrially relevant examples with many design variables to demonstrate the effectiveness of the adjoint method on Cartesian meshes.

Nemec, Marian↗
NASA NTRS1992

LDEF mechanical systems

Following LDEF retrieval, a number of studies were made of mechanical hardware and structure flown on the LDEF. The primary objectives are to determine the effects of long term space exposure on (1) mechanisms either used on LDEF or as part of individual experiments; (2) LDEF structural components; and (3) fasteners. Results from examination and testing of LDEF structure, fasteners, LDEF end support beam, environment exposure control canisters, experiment tray clamps, LDEF grapple fixtures, and viscous damper are presented. The most significant finding is the absence of space exposure related cold welding. The instances of seizure or removal difficulties initially attributed to cold welding were shown to have resulted from installation galling damage or improper removal techniques. Widespread difficulties encountered with removal of stainless steel fasteners underscore the need for effective thread lubrication schemes to ensure successful application of proposed orbital replacement units onboard Space Station Freedom.

W Steve Spear↗
NASA NTRS1988

Effects of excitation level on the stability of an axisymmetric mixing layer

The effect of various levels of excitation on the stability and development of an axisymmetric mixing layer was studied experimentally. The flow was excited axisymmetrically by a single speaker placed at the base of the plenum chamber. Measurements of mean and phase-averaged velocity profiles were made using an array of hot-wire probes. The measured profiles were compared to eigenfunctions calculated from linear, viscous stability theory. It is shown that the theoretical predictions, based on measured profiles of mean velocity, compare very well with the phase-averaged measurements, even when the local disturbance reaches levels as high as 24 percent of the jet speed. The cumulative effect of excitation on the mean flow is examined as a function of local Strouhal number as well as excitation level.

Samet, M. M.↗
NASA NTRS1988

Fluid dynamic modeling and numerical simulation of low-density hypersonic flow

The concept of a viscous shock-layer and several related versions of continuum theories/methods are examined for their adequacy as a viable framework to study flow physics and aerothermodynamics of relevance to sustained hypersonic flights. Considering the flat plate at angle of attack, or the wedge, as a generic example for the major aerodynamic component of a hypersonic vehicle, the relative importance of the molecular-transport effects behind the shock (in the form of the 'shock slip') and the wall-slip effects are studied. In the flow regime where the shock-transition-zone thickness remains small compared to the shock radius of curvature, a quasi-one-dimensional shock structure under the Burnett/thirteen-moment approximation, as well as particulate/collisional models, can be consistently developed. The fully viscous version of the shock-layer model is shown to provide the crucial boundary condition downstream the shock in this case. The gas-kinetic basis of the continuum description for the flow behind the bow shock, and certain features affecting the non-equilibrium flow chemistry, are also discussed.

Cheng, H. K.↗
DOE OSTI2023

Sensitivity measurements for a 250 MHz quartz shear-horizontal surface acoustic wave biosensor under liquid viscous loading

Surface acoustic wave (SAW) devices have been used in biochemical assays due to their high sensitivity. The device sensitivity is a function of changes in the density and viscosity of the liquid. Here, we studied the effect of fluid viscosity using a 250 MHz quartz shear-horizontal (SH)-SAW biosensor by monitoring different concentrations of binary aqueous/glycerol solutions. In this study, the sensitivity of the biosensor was determined by fitting the data to models derived from perturbation theory. Measurements in water were used as the reference. For a 0% to 50% glycerol solution, an 87°–204° separation in the phase shift was observed. The slope of the plot of the phase shift vs (ηρ)0.5 was used to indicate the sensor’s sensitivity. The sensitivity for our 250 MHz quartz SH-SAW sensors was calculated to be 3.7×10−3m2sKg. The corresponding mass sensitivity was determined to be 9.25 × 105m2Kg. The limit of detection was calculated to be 36 picograms (pg), while the limit of quantification or LOQ was calculated to be 109 pg. Traditionally, liquid phase measurements have been challenging for SAW devices because liquids dampen the vibrating sensors severely. This problem has been largely solved using a transverse (shear) wave instead of the more popular longitudinal or Rayleigh waves. Liquid measurements are now possible using transverse waves, also known as shear waves, because transverse waves are only minimally attenuated by liquids. Shear-horizontal SAW sensors (SH-SAW) show great promise as label-free biosensors because of their ability to handle liquid samples. However, the viscosity of the liquid still induces loading effects and can be measured when the liquid is loaded onto the SH-SAW propagating surface (delay line). When the liquid above the delay line is perturbed by physical or chemical changes, such as binding to a receptor, it alters the propagating acoustic wave. The SH-SAW device can measure these changes in liquid properties as a change in the wave’s phase compared to the original wave. The device’s phase shift was recorded as a function of the changes in the density and viscosity of the binary glycerol solution and used to determine the sensitivity in the linear dynamic range of responses.

Materials Science↗
NASA NTRS2001

Influence of Solutocapillary Convection on Macrovoid Defect Formation in Polymeric Membranes

Macrovoids (MVs) are large (10-50 micrometers) pores often found in polymeric membranes prepared via phase-inversion techniques. They are generally considered undesirable, as they adversely affect the permeability properties and performance of polymeric membranes for microfiltration, ultrafiltration, and reverse osmosis. However, MVs can be useful in certain thin-film applications in which vapor transmission is necessary, or for use as reservoirs for enzymes or liquid membrane material. If more could be learned about the nature and causes of MV formation, it might be possible to devise techniques to control and/or prevent MV formation that are more effective than those currently employed. Two hypotheses for the MV growth mechanism have been advanced. Reuvers proposed that once initiated, MV growth can be attributed to diffusion of (primarily) solvent to the MV nuclei. Because this mechanism does not involve gross movement of the MV, the presence or absence of body forces such as buoyancy should not significantly affect MV growth. On the other hand, Shojaie et al. proposed that solutocapillary convection induced by a steep surface-tension gradient along the MV/bulk solution interface enhances mass transfer to the growing MV. This interfacial convection exerts a force that pulls the growing MV downward into the casting solution. Both buoyancy and viscous drag hinder MV growth by inhibiting this motion. Thus, removing the buoyancy force by casting in microgravity should augment MV growth according to this hypothesis. Whereas neither surface tension nor gravity has a significant effect on MV growth according to the first hypothesis, buoyancy forces should be important if the second hypothesis is correct. The overall goal of this research is to test these two hypotheses in order to improve our understanding of the MV growth processing solvent-cast polymeric membranes. Studying MV growth in low-gravity conditions is pivotal to our ability to discriminate between these two hypotheses.

Pekny, M. R.↗
NASA NTRS2001

A Novel Approach for Reducing Rotor Tip-Clearance Induced Noise in Turbofan Engines

Rotor tip-clearance induced noise, both in the form of rotor self noise and rotor-stator interaction noise , constitutes a significant component of total fan noise. Innovative yet cost effective techniques to suppress rotor-generated noise are, therefore, of foremost importance for improving the noise signature of turbofan engines. To that end, the feasibility of a passive porous treatment strategy to positively modify the tip-clearance flow field is addressed. The present study is focused on accurate viscous flow calculations of the baseline and the treated rotor flow fields. Detailed comparison between the computed baseline solution and experimental measurements shows excellent agreement. Tip-vortex structure, trajectory, strength, and other relevant aerodynamic quantities are extracted from the computed database. Extensive comparison between the untreated and treated tip-clearance flow fields is performed. The effectiveness of the porous treatment for altering the rotor-tip vortex flow field in general and reducing the intensity of the tip vortex, in particular, is demonstrated. In addition, the simulated flow field for the treated tip clearly shows that substantial reduction in the intensity of both the shear layer roll-up and boundary layer separation on the wall is achieved.

Khorrami, Mehdi R.↗
NASA NTRS1995

Effect of Baffle on Gravity-Gradient-Excited Slosh Waves and Spacecraft Moment and Angular-Momentum Fluctuations in Microgravity

The dynamical behavior of fluids affected by the asymmetric gravity gradient acceleration has been investigated. In particular, the effects of surface tension on partially filled rotating fluids applicable to a full-scale Gravity Probe-B Spacecraft dewar tank with and without baffles are studied. Results of slosh wave excitation along the liquid-vapor interface induced by gravity gradient acceleration indicate that the gravity gradient acceleration is equivalent to the combined effect of a twisting force and a torsional moment acting on the spacecraft. The results are clearly seen from one-up one-down and one-down one-up oscillations in the cross-section profiles of two bubbles in the vertical (r, z)-plane of the rotating dewar, and from the eccentric contour of the bubble rotating around the axis of the dewar in a horizontal (r, theta)-plane. As the viscous force, between liquid and solid interface, greatly contributes to the damping of slosh wave excitation, a rotating dewar with baffles provides more areas of liquid-solid interface than that of a rotating dewar without baffles. Results show that the damping effect provided by the baffles reduces the amplitude of slosh wave excitation and lowers the degree of asymmetry in liquid-vapor distribution. Fluctuations of angular momentum and fluid moment caused by the slosh wave excited by gravity gradient acceleration with and without baffle boards are also investigated. It is also shown that the damping effect provided by the baffles greatly reduces the amplitudes of angular momentum and fluid moment fluctuations.

Hung, R. J.↗
NASA NTRS2002

Progress Toward Generation of a Navier-Stokes Database for a Harrier in Ground Effect

The Harrier YAV-8B aircraft is capable of vertical and short-field take-off and landing (V/STOL) by directing its four exhaust nozzles toward the ground, or conventional flight by rotating its nozzles into a horizontal position. The British Royal Air Force and the United States Marine Corps have used this aircraft for more than 30 years to provide a quick reaction time for troop support, and reduce the need for long runways. The success of this powered-lift (PL) vehicle has also prompted the more recent design of the Joint Strike Fighter (JSF). However there are significant safety issues that must be addressed when operating a PL vehicle in close proximity to the ground. Hot Gas Ingestion (HGI) by the inlets can result in a rapid loss of powered lift; and high-speed jet flows along the ground plane can induce low pressures underneath the vehicle, causing a 'suck-down' effect. Under these conditions, departure from controlled flight may occur. Moreover, unsteady ground vortices and jet fountains can affect the aircraft,s controllability and its proximity to ground troops. The viscous, time-dependent flow fields of PL vehicles are difficult to accurately and efficiently predict using Computational Fluid Dynamics (CFD). A number of researchers have used the time-dependent Reynolds-averaged Navier-Stokes (RANS) equations to compute flows for single and multiple jets in a cross-flow. A few have added some geometric complexity to the problem by computing flows for jet-augmented delta wings near a ground plane. Smith et.al. computed for the first time a single RANS solution about a simplified Harrier. This geometry included a fuselage, wing, leading edge root extension (LERX), inlets, and exhaust nozzles. All of these investigations cite two practical problems with computing these flows: 1) the need for improved solution accuracy; and, 2) the need for faster solution methods. We view the need for faster solution methods as key to improving the solution accuracy and making this class of computation more routine. One can hardly refine grids, explore the use of advanced turbulence models, and generate databases when it takes weeks of dedicated computer time for a single solution. Chaderjian, Ahmad, Pandya, and Murman have focused on reducing the time-to-solution for this very difficult and complex problem through process automation and exploitation of parallel computing. They began with the Harrier geometry reported, and added a deflected wing flap and empennage for greater realism. To date more than 80 solutions have been carried out. This paper will describe this process and progress made in reducing the time required to generate a simple longitudinal force and moment database for a Harrier in ground effect. It shows a typical snap-shot from an unsteady streakline animation, where fluid particles are colored by temperature. The ground vortex and a jet-fountain vortex are highlighted. It also shows a similar streakline image, where HGI occurs due to the vehicle in close proximity to the ground. It is show the mean lift coefficient as a function of angle of attack and height. The angle of attack range was 4 deg less than or = alpha less than or = 10 deg with an increment of 1 degree, and the height range was 10 ft less than or = h less than or = 30ft with an increment of 5 feet. This 35 solution database was extended to over 2500 cases using a monotone cubic-spline interpolation procedure. The suck-down effect (reduction of lift near the ground) is highlighted in the figure. The "cushion effect," the conventional reduction of lift as the vehicle moves out of ground effect, is also indicated. All 35 RANS solutions were obtained using 952 Silicon Graphics Origin 2000 and 3000 processors in dedicated mode for one week. Typically, 112 processors were assigned to each case. Some other cases used fewer processors to utilize all available CPUS. The final paper will report on the automation of the solution process, including: grid generation, job monitoring, solution completion criteria, and post processing. Moreover, improvements in parallel efficiency for a dual time-step algorithm for the RANS equations will also be presented. Results will be discussed in detail using unsteady streakline flow visualization to correlate unsteady flow structures with dominant aerodynamic frequencies. The stability derivatives, CL, and CL, will also be presented.

Chaderjian, Neal M.↗
DOE OSTI2024

Applying a Phase-Separation Parameterization in Modeling Secondary Organic Aerosol Formation from Acid-Driven Reactive Uptake of Isoprene Epoxydiols under Humid Conditions

Secondary organic aerosol (SOA) from acid-driven reactive uptake of isoprene epoxydiols (IEPOX) contributes up to 40% of organic aerosol (OA) mass in fine particulate matter. Our previous work showed substantial conversions of particulate inorganic sulfates to surface-active organosulfates (OSs) by IEPOX decreases aerosol acidity and creates a viscous organic-rich shell that poses as a diffusion barrier, inhibiting additional reactive uptake of IEPOX. In this study, to account for this “self-limiting” effect, a phase-separation box model was developed to evaluate parameterizations of IEPOX reactive uptake against time-resolved chamber measurements of IEPOX-SOA tracers, including 2-methyltetrols (2-MT) and methyltetrol sulfates (MTS), at ~ 50% relative humidity. The phase-separation model was most sensitive to mass accommodation coefficient, IEPOX diffusivity in the organic shell, and ratio of the third-order reaction rate constants forming 2-MT and MTS (k MT /k MTS ). In particular, k MT /k MTS had to be lower than 0.1 to bring model predictions of 2-MT and MTS in closer agreement with chamber measurements, while prior studies reported values larger than 0.71. The model-derived rate constants favor more particulate MTS formation due to 2-MT likely off-gassing at ambient-relevant OA loadings. Incorporating this parametrization into chemical transport models is expected to predict lower IEPOX-SOA mass and volatility due to the predominance of OSs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Weak collisionless shocks mediated by ion gyroviscosity

Collisionless shocks are ubiquitous in space and astrophysical plasmas, and they are essential dynamical features of these systems. Lacking Coulomb collisions, these shocks are mediated by the anomalous dissipation provided by nonlinear plasma instabilities. By numerically resolving the structure of a steady-state, ion gyroviscous shock, we show that ion gyroviscosity, alone, can produce weak (M≲1.1, where M is the sonic Mach number) shocks in a collisionless, magnetized plasma. We emphasize that this effect does not require an appeal to plasma microturbulence. Moreover, while most collisionless systems may be unsuitable to support purely gyroviscous shocks, we argue that gyro-viscous heating may be an overlooked mechanism, generally; and it may be a key driver within magnetohydrodynamic shocks at large. In conclusion, representative examples include the plasma environments produced on the plasma liner experiment and the magnetized liner inertial fusion platforms.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1985

Investigation of parabolic computational techniques for internal high-speed viscous flows

A feasibility study was conducted to assess the applicability of an existing parabolic analysis (ADD-Axisymmetric Diffuser Duct), developed previously for subsonic viscous internal flows, to mixed supersonic/subsonic flows with heat addition simulating a SCRAMJET combustor. A study was conducted with the ADD code modified to include additional convection effects in the normal momentum equation when supersonic expansion and compression waves were present. It is concluded from the present study that for the class of problems where strong viscous/inviscid interactions are present a global iteration procedure is required.

Anderson, O. L.↗
NASA NTRS1984

Thermal evolution of Venus

A modification of the Boussinesq fluid assumption is the basis of the present theory of three-dimensional and finite amplitude convection in a viscous spherical shell with temperature- and pressure-dependent physical parameters. The theory is applied to the definition of thermal evolution models for Venus which emphasize the effects of certain physical parameters on thermal evolution, rather than the specific thermal history of the planet. It is suggested that a significant portion of the present temperature in the mantle and surface heat flux of Venus is due to the decay of a high temperature that was established in the planet at the completion of its core formation, and that Venus has been highly convective over the course of its history, until about 0.5 Ga ago.

Arkani-Hamed, J.↗
NASA NTRS1985

Numerical investigation of internal high-speed viscous flows using a parabolic technique

A feasibility study has been conducted to assess the applicability of an existing parabolic analysis (ADD-Axisymmetric Diffuser Duct), developed previously for subsonic viscous internal flows, to mixed supersonic/subsonic flows with heat addition simulating a SCRAMJET combustor. A study was conducted with the ADD code modified to include additional convection effects in the normal momentum equation when supersonic expansion and compression waves are present. A set of test problems with weak shock and expansion waves have been analyzed with this modified ADD method and stable and accurate solutions were demonstrated provided the streamwise step size was maintained at levels larger than the boundary layer displacement thickness. Calculations made with further reductions in step size encountered departure solutions consistent with strong interaction theory. Calculations were also performed for a flow field with a flame front in which a specific heat release was imposed to simulate a SCRAMJET combustor. In this case the flame front generated relatively thick shear layers which aggravated the departure solution problem. Qualitatively correct results were obtained for these cases using a marching technique with the convective terms in the normal momentum equation suppressed. It is concluded from the present study that for the class of problems where strong viscous/inviscid interactions are present a global iteration procedure is required.

Anderson, O. L.↗