A power-series solution for the unsteady laminar boundary-layer flow in an expansion wave of finite width moving through a gas initially at rest
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This paper (the first in a series) focuses on using active-control methods to maintain laminar flow in a region of the flow in which the natural instabilities, if left unattended, lead to turbulent flow. The authors review previous studies that examine wave cancellation (currently the most prominent method) and solve the unsteady, nonlinear Navier-Stokes equations to evaluate this method of controlling instabilities. It is definitely shown that instabilities are controlled by the linear summation of waves (i.e., wave cancellation). Although a mathematically complete method for controlling arbitrary instabilities has been developed (but not yet tested), the review, duplication, and physical explanation of previous studies are important steps for providing an independent verification of those studies, for establishing a framework for subsequent work which will involve automated transition control, and for detailing the phenomena by which the automated studies can be used to expand knowledge of flow control.
During the course of this investigation, the following two topics were studied theoretically: (1) forced convection and sedimentation past a flat plate, and (2) the effect of rain on airfoil performance. The prototype of the first topic is that of air flowing past the wing section of an aircraft under heavy rain and high windshear. The long-range objective of this project was to identify the various factors determining the dynamics of the flow and then to develop a theoretical framework for modeling such systems. The second topic focused on the idea that the presence of the gas-liquid interface (being the air flow around the airfoil and the thin liquid film created by the rain) accelerates flow separation and thus induces performance losses.
The general objective of the present work is to explore the use of Rapid Distortion Theory (RDT) in analysis of the two-point statistics of the log-layer. RDT is applicable only to unsteady flows where the non-linear turbulence-turbulence interaction can be neglected in comparison to linear turbulence-mean interactions. Here we propose to use RDT to examine the structure of the large energy-containing scales and their interaction with the mean flow in the log-region. The contents of the work are twofold: First, two-point analysis methods will be used to derive the law-of-the-wall for the special case of zero mean pressure gradient. The basic assumptions needed are one-dimensionality in the mean flow and homogeneity of the fluctuations. It will be shown that a formal solution of the two-point correlation equation can be obtained as a power series in the von Karman constant, known to be on the order of 0.4. In the second part, a detailed analysis of the two-point correlation function in the log-layer will be given. The fundamental set of equations and a functional relation for the two-point correlation function will be derived. An asymptotic expansion procedure will be used in the log-layer to match Kolmogorov's universal range and the one-point correlations to the inviscid outer region valid for large correlation distances.
Laminar film condensation under the simultaneous influence of gas-liquid interface shear and body force (g force) is analyzed over a flat plate. Important parameters governing condensation and heat transfer of pure vapor are determined. Mixtures of condensable vapor and noncondensable gas are also analyzed. The conditions under which the body force has a significant influence on condensation are determined.
Experimental work with leading edge separation bubbles is presented to clarify the issues regarding transition in separated regions. Hot-wire measurements, in the form of oscilloscope traces, turbulence intermittency and conditionally sampled velocity distributions are given. The resulting points of transition onset and spot production rates are compared to existing correlations.
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APS March Meeting 2022, Virtual, March 13-18, 2022
2022 Society for Industrial and Applied Mathematics Annual Meeting, Pittsburgh, PA, July 11-15, 2022
Boundary-layer bleed in supersonic inlets is typically used to avoid separation from adverse shock-wave/boundary-layer interactions and subsequent total pressure losses in the subsonic diffuser and to improve normal shock stability. Methodologies used to determine bleed requirements are reviewed. Empirical sonic flow coefficients are currently used to determine the bleed hole pattern. These coefficients depend on local Mach number, pressure ratio, hole geometry, etc. A new analytical bleed method is presented to compute sonic flow coefficients for holes and narrow slots and predictions are compared with published data to illustrate the accuracy of the model. The model can be used by inlet designers and as a bleed boundary condition for computational fluid dynamic studies.
Boundary layer flow and turbulence transport analyses to study the influence of the free-stream turbulence on the surface heat transfer rate and the skin friction around the stagnation point of a circular cylinder in a turbulent flow are presented. The analyses are formulated with the turbulent boundary layer equations, the Reynolds stress transport equations and the k - epsilon two-equation turbulence modeling. The analyses are used to calculate the time-averaged turbulence double correlations, the mean flow properties, the surface heat transfer rate and the skin friction with an isotropic turbulence in the freestream. The analytical results are described and compared with the existing experimental measurements. Depending on the free-stream turbulence properties, the turbulence kinetic energy can increase or decrease as the flow moves toward the surface. However, the turbulence kinetic energy induces large Reynolds normal stresses at the boundary layer edge. The Reynolds normal stresses change the boundary layer profiles of the time-averaged double correlations of the velocity and temperature fluctuations, the surface heat transfer rate and the skin friction. The free-stream turbulence dissipation rate can affect the stagnation-point heat transfer rate but the influence of the free-stream temperature fluctuation on the heat transfer rate is insignificant.
Boundary layer in nozzle of arc-heated wind tunnel, obtaining velocity, temperature and density profiles
The implementation and validation of the Chien low Reynolds number k-epsilon turbulence model in the two dimensional axisymmetric version Proteus, a compressible Navier-Stokes computer code, are presented. The set of k-epsilon equations are solved by marching in time using a coupled alternating direction implicit (ADI) solution procedure with generalized first or second order time differencing. To validate Proteus and the k-epsilon turbulence model, laminar and turbulent computations were done for several benchmark test cases: incompressible fully developed 2-D channel flow; fully developed axisymmetric pipe flow; boundary layer flow over a flat plate; and turbulent Sajben subsonic transonic diffuser flows. Proteus results from these test cases showed good agreement with analytical results and experimental data. Detailed comparisons of both mean flow and turbulent quantities showed that the Chien k-epsilon turbulence model given good results over a wider range of turbulent flow than the Baldwin-Lomax turbulence model in the Proteus code with no significant CPU time penalty for more complicated flow cases.
Boundary layer trip geometry, size and location effects on position of transition at hypersonic speeds
Turbulent boundary layer laminarization in conical nozzle flow, measuring velocity profiles and friction coefficient