Development of an approximation analysis for the laminar boundary layer behind a moving shock wave
Approximation analysis for laminar two dimensional boundary layer behind plane shock wave moving over infinite flat plate
Abbott, D. E.↗
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Base Pressure at Supersonic Speeds on Two-dimensional Airfoils and on Bodies of Revolution with and Without Fins Having Turbulent Boundary Layers
An analysis has been made of available experimental data to show the effects of most of the variables that are more predominant in determining base pressure at supersonic speeds. The analysis covers base pressures for two-dimensional airfoils and for bodies of revolution with and without stabilizing fins and is restricted to turbulent boundary layers. The present status of available experimental information is summarized as are the existing methods for predicting base pressure. A simple semiempirical method is presented for estimating base pressure. For two-dimensional bases, this method stems from an analogy established between the base-pressure phenomena and the peak pressure rise associated with the separation of the boundary layer. An analysis made for axially symmetric flow indicates that the base pressure for bodies of revolution is subject to the same analogy. Based upon the methods presented, estimations are made of such effects as Mach number, angle of attack, boattailing, fineness ratio, and fins. These estimations give fair predictions of experimental results. (author)
LOVE EUGENE S↗
A computationally efficient modelling of laminar separation bubbles
The goal of this research is to accurately predict the characteristics of the laminar separation bubble and its effects on airfoil performance. To this end, a model of the bubble is under development and will be incorporated in the analysis section of the Eppler and Somers program. As a first step in this direction, an existing bubble model was inserted into the program. It was decided to address the problem of the short bubble before attempting the prediction of the long bubble. In the second place, an integral boundary-layer method is believed more desirable than a finite difference approach. While these two methods achieve similar prediction accuracy, finite-difference methods tend to involve significantly longer computer run times than the integral methods. Finally, as the boundary-layer analysis in the Eppler and Somers program employs the momentum and kinetic energy integral equations, a short-bubble model compatible with these equations is most preferable.
Maughmer, Mark D.↗
A comparison of numerical flux formulas for the Euler and Navier-Stokes equations
Numerical flux formulas for the convection terms in the Euler or Navier-Stokes equations are analyzed with regard to their accuracy in representing steady nonlinear and linear waves (shocks and entropy/shear waves, respectively). Numerical results are obtained for a one-dimensional conical Navier-Stokes flow including both a shock and a boundary layer. Analysis and experiments indicate that for an accurate representation of both layers the flux formula must include information about all different waves by which neighboring cells interact, as in Roe's flux-difference splitting. In comparison, Van Leer's flux-vector splitting, which ignores the linear waves, badly diffuses the boundary layer. The results of MacCormack's scheme, if properly tuned, are significantly better. The use of a sufficiently detailed flux formula appears to reduce the number of cells required to resolve a boundary layer by a factor 1/2 to 1/4 and thus pays off.
Van Leer, Bram↗
Transonic CFD applications at Boeing
The use of computational methods for three dimensional transonic flow design and analysis at the Boeing Company is presented. A range of computational tools consisting of production tools for every day use by project engineers, expert user tools for special applications by computational researchers, and an emerging tool which may see considerable use in the near future are described. These methods include full potential and Euler solvers, some coupled to three dimensional boundary layer analysis methods, for transonic flow analysis about nacelle, wing-body, wing-body-strut-nacelle, and complete aircraft configurations. As the examples presented show, such a toolbox of codes is necessary for the variety of applications typical of an industrial environment. Such a toolbox of codes makes possible aerodynamic advances not previously achievable in a timely manner, if at all.
Tinoco, E. N.↗
Comparison of a quasi-3D analysis and experimental performance for three compact radial turbines
An experimental aerodynamic evaluation of three compact radial turbine builds was performed. Two rotors which were 40 to 50 percent shorter in axial length than conventional state of the art radial rotors were tested. A single nozzle design was used. One rotor was tested with the nozzle at two stagger angle settings. A second rotor was tested with the nozzle in only the closed down setting. Experimental results were compared to predict results from a quasi-3D inviscid and boundary layer analysis, called Meridl/Tsonic/Blayer (MTSB). This analysis was used to predict turbine performance. It has previously been calibrated only for axial, not radial, turbomachinery. The predicted and measured efficiencies were compared at the design point for the three turbines. At the design points the analysis overpredicted the efficiency by less than 1.7 points. Comparisons were also made at off-design operating points. The results of these comparisons showed the importance of an accurate clearance model for efficiency predictions and also that there are deficiencies in the incidence loss model used.
Simonyi, P. S.↗
Comparison of a quasi-3D analysis and experimental performance for three compact radial turbines
An experimental aerodynamic evaluation of three compact radial turbine builds was performed. Two rotors which were 40-50 percent shorter in axial length than conventional state-of-the-art radial rotors were tested. A single nozzle design was used. One rotor was tested with the nozzle at two stagger angle settings. A second rotor was tested with the nozzle in only the closed down setting. Experimental results were compared to predicted results from a quasi-3D inviscid and boundary layer analysis, called MTSB (Meridl/Tsonic/Blayer). This analysis was used to predict turbine performance. It has previously been calibrated only for axial, not radial, turbomachinery. The predicted and measured efficiencies were compared at the design point for the three turbines. At the design points the analysis overpredicted the efficiency by less than 1.7 points. Comparisons were also made at off-design operating points. The results of these comparisons showed the importance of an accurate clearance model for efficiency predictions and also that there are deficiencies in the incidence loss model used.
Simonyi, P. S.↗
Determination of general relations for the behavior of turbulent boundary layers
An analysis has been made of a considerable amount of data for turbulent boundary layers along wings and bodies of various shapes in order to determine the fundamental variables that control the development of turbulent boundary layers. It was found that the type of velocity distribution in the boundary layer could be expressed in terms of a single parameter. This parameter was chosen as the ratio of the displacement thickness to the momentum thickness of the boundary layer. The variables that control the development of the turbulent boundary layer apparently are: (1) the ratio of the nondimensional pressure gradient, expressed in terms of the local dynamic pressure outside the boundary layer and boundary-layer thickness, to the local skin-friction coefficient and (2) the shape of the boundary layer. An empirical equation has been developed in terms of these variables that, when used with the momentum equation and the skin-friction relation, makes it possible to trace the development of the turbulent boundary layer to the separation point.
Von Doenhoff, Albert E↗
Transonic analysis of canted winglets
A computational method developed to provide a transonic analysis for upper/lower surface wing-tip mounted winglets is described. Winglets with arbitrary planform, cant and toe angle, and airfoil section can be modeled. The embedded grid approach provides high flow field resolution and the required geometric flexibility. In particular, coupled Cartesian/cylindrical grid systems are used to model the complex geometry presented by canted upper/lower surface winglets. A new rotated difference scheme is introduced in order to maintain the stability of the small-disturbance formulation in the presence of large spanwise velocities. Wing and winglet viscous effects are modeled using a two-dimensional 'strip' boundary layer analysis. Correlations with wind tunnel and flight test data for three transport configurations are included.
Rosen, B. S.↗
Assessment of a parabolic analysis for axisymmetric internal flows in rocket and turbomachinery ducts
The flow paths in gas turbine passages encompass a wide range of flow properties such as Reynolds number and Mach number as well as many other variable flow conditions such as swirl, free-stream turbulence, and laminar/turbulent transition. An existing computer program, the Axisymmetric Diffuser Duct (ADD) code, which calculates compressible, turbulent, swirling flow through axisymmetric ducts has been modified to include the effects of free-stream turbulence and laminar/turbulent transition. The program has been evaluated on a matrix of test cases to determine its accuracy, robustness, and limits of applicability. This improved version of the ADD code calculates solutions which compare well with available data and can now be applied to a wider range of problems than previously possible. In addition a concept called local enhancement was developed and tested on a simple two-dimensional geometry in order to demonstrate a method to reduce computer time. In this concept the pressure distribution is calculated on a coarse grid using the ADD code and the viscous layer is locally enhanced using a boundary layer analysis. By applying this concept, an order of magnitude reduction in computer time was possible without any loss in accuracy.
Power, G. D.↗
Use of tritium-rich fuel to improve the yield of layered deuterium/tritium inertial fusion capsules
In deuterium–tritium (DT) ice layered implosions, nearly all hot spot mass at peak burn comes from the dense fuel. Accurate prediction of the fuel mass ablation, including the enthalpy associated with mass inflow into the hot spot from the dense fuel, is essential to understanding the energetics and ignition of the hot spot in layered implosions. A recently published boundary layer analysis (Daughton et al., 2023) indicates a faster mass ablation rate than in previous analyses of layered implosions. Inclusion of this effect provides a better match to simulations and leads to a new ignition threshold where the temperature of the dense fuel plays a critical role. This analysis motivates possible new directions for improved capsule performance. Here, the authors present evidence in support of one such approach: the use of tritium-rich ice to decrease 14 MeV neutron scattering and heating of the dense fuel, resulting in less mass ablation and more robust burn of the hot spot. It is found from numerical simulations that despite a less favorable D:T ratio in the ice, the use of a 40:60 D:T ratio leads to an increase in capsule yield of 17% percent compared with that of a 50:50 D:T ratio fuel for capsules resembling those of the recent N210808 ignition experiment on the NIF (Abu-Shawareb et al., 2022) and an increase of 74% compared with that of a 60:40 D:T ratio fuel capsule. Finally, these results are potentially important for modeling all layered implosions, since some degree of DT fractionization may arise naturally during the beta layering process. In addition, this physics is important for the feasibility of high-gain capsule designs that seek to minimize tritium usage, as in some inertial fusion energy concepts.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Convective heat transfer in a high aspect ratio minichannel heated on one side
Experimental results are presented for single-phase heat transfer in a narrow rectangular minichannel heated on one side. The aspect ratio and gap thickness of the test channel were 29:1 and 1.96 mm, respectively. Friction pressure drop and Nusselt numbers are reported for the transition and fully turbulent flow regimes, with Prandtl numbers ranging from 2.2 to 5.4. Turbulent friction pressure drop for the high aspect ratio channel is well-correlated by the Blasius solution when a modified Reynolds number, based upon a laminar equivalent diameter, is utilized. The critical Reynolds number for the channel falls between 3500 and 4000, with Nusselt numbers in the transition regime being reasonably predicted by Gnielinski's correlation. The dependence of the heat transfer coefficient on the Prandtl number is larger than that predicted by circular tube correlations, and is likely a result of the asymmetric heating. The problem of asymmetric heating condition is approached theoretically using a boundary layer analysis with a two-region wall layer model, similar to that originally proposed by Prandtl. The analysis clarifies the influence of asymmetric heating on the Nusselt number and correctly predicts the experimentally observed trend with Prandtl number. Furthermore, a semi-analytic correlation is derived from the analysis that accounts for the effect of aspect ratio and asymmetric heating, and is shown to predict the experimental results of this study with a mean absolute error (MAE) of less than 5% for 4000 < Re < 70,000.
42 ENGINEERING↗
Heat and mass transfer in dispersed, two-phase, single-component flow
Laminar boundary layer analysis of heat and mass transfer in dispersed two phase flow over heated surface
Jones, M. C.↗
Heat transfer to insulator wall of linear MGD accelerator
Heat transfer to insulator wall of linear MGD accelerator attached to shock tube, comparing measurements with Hartmann boundary layer analysis
Cochran, R. A.↗
Comparison of experimental and analytical results for a 20-MW combustion-driven Hall configuration MHD generator
Combustion driven Hall configuration MHD generator, discussing boundary layer analysis, gas density nonuniformity and electrode drop
Brogan, T. R.↗
A numerical investigation of film cooling as an alternate thermal protection system for spacecraft during atmospheric reentry
Research was undertaken to determine the mass required to protect a surface during atmospheric reentry by injecting a cold gas tangentially along the surface. A consideration of this problem revealed that the boundary layer equations could be employed to approximate the most important flow configurations which occur in film cooling. However, even with this simplification, the equations to be solved are complex, nonlinear, coupled partial differential equations. Due to the relative weakness of classical methods of boundary layer analysis, finite difference methods were chosen as the best approach to the formidable problem under consideration. Instead of blindly adopting a proposed technique and trying to force it to the problem, a more systematic study was deemed to be not only desirable but necessary. A relatively basic study of the application of finite difference methods was undertaken with the objective of developing an algorithm capable of obtaining accurate solutions to film cooling problems.
Clausing, A. M.↗
State space approach to mixed boundary value problems.
A state-space procedure for the formulation and solution of mixed boundary value problems is established. This procedure is a natural extension of the method used in initial value problems; however, certain special theorems and rules must be developed. The scope of the applications of the approach includes beam, arch, and axisymmetric shell problems in structural analysis, boundary layer problems in fluid mechanics, and eigenvalue problems for deformable bodies. Many classical methods in these fields developed by Holzer, Prohl, Myklestad, Thomson, Love-Meissner, and others can be either simplified or unified under new light shed by the state-variable approach. A beam problem is included as an illustration.
Chen, C. F.↗
Electron collection theory for a D-region subsonic blunt electrostatic probe
Blunt probe theory for subsonic flow in a weakly ionized and collisional gas is reviewed, and an electron collection theory for the relatively unexplored case, Deybye length approximately 1, which occurs in the lower ionosphere (D-region), is developed. It is found that the dimensionless Debye length is no longer an electric field screening parameter, and the space charge field effect can be negelected. For ion collection, Hoult-Sonin theory is recognized as a correct description of the thin, ion density-perturbed layer adjacent the blunt probe surface. The large volume with electron density perturbed by a positively biased probe renders the usual thin boundary layer analysis inapplicable. Theories relating free stream conditions to the electron collection rate for both stationary and moving blunt probes are obtained. A model based on experimental nonlinear electron drift velocity data is proposed. For a subsonically moving probe, it is found that the perturbed region can be divided into four regions with distinct collection mechanisms.
Wai-Kwong Lai, T.↗