This work considers the compressible flow field established in a rectangular porous channel. Our treatment is based on a Rayleigh–Janzen perturbation applied to the inviscid steady two-dimensional isentropic flow equations. Closed-form expressions are then derived for the main properties of interest. Our analytical results are verified via numerical simulation, with laminar and turbulent models, and with available experimental data. They are also compared to existing one-dimensional theory and to a previous numerical pseudo-one-dimensional approach. Our analysis captures the steepening of the velocity profiles that has been reported in several studies using either computational or experimental approaches. Finally, explicit criteria are presented to quantify the effects of compressibility in two-dimensional injection-driven chambers such as those used to model slab rocket motors.
In this paper, we discuss the merits of two models for the swirl velocity in the core of a confined bidirectional vortex. The first is piecewise, Rankine-like, based on a combinedvortex representation. It stems from the notion that a uniform shear stress distribution may be assumed in the inner vortex region of a cyclone, especially at high Reynolds numbers. Thereafter, direct integration of the shear stress enables us to retrieve an expression for the swirl velocity that overcomes the inviscid singularity at the centreline. The second model consists of a modified asymptotic solution to the problem obtained directly from the Navier-Stokes equations. Both solutions we present transition smoothly to the outer, free-vortex approximation at some intermediate position in the chamber. This position is deduced from available experimental data to the extent of providing an accurate swirl velocity distribution throughout the chamber. By scaling the constant shear radius to the core layer thickness, the constant of proportionality is readily calculated using the method of least squares. Interestingly, the constant of proportionality is found to be invariant at several vortex Reynolds numbers, thus helping to achieve closure. The combined-vortex representation is validated against a large body of experimental measurements and through comparisons to a laminar core model that is enhanced through the use of an eddy viscosity. Other heuristic schemes are discussed and the two most suitable models to capture realistic flow behaviour at high vortex Reynolds numbers are identified. Our two models are first derived analytically and then anchored on the available experimental measurements.
The object of this study is to canvas the literature for the purpose of identifying and compiling a list of Gaps, Obstacles, and Technological Challenges in Hypersonic Applications (GOTCHA). The significance of GOTCHA related deficiencies is discussed along with potential solutions, promising approaches, and feasible remedies that may be considered by engineers in pursuit of next generation hypersonic vehicle designs and optimizations. Based on the synthesis of several modern surveys and public reports, a cohesive list is formed consisting of widely accepted areas needing improvement that fall under several general categories. These include: aerodynamics, propulsion, materials, analytical modeling, CFD modeling, and education in high speed flow physics. New methods and lines of research inquiries are suggested such as the homotopy-based analysis (HAM) for the treatment of strong nonlinearities, the use of improved turbulence models and unstructured grids in numerical simulations, the need for accessible validation data, and the refinement of mission objectives for Hypersonic Airbreathing Propulsion (HAP).
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