CFD Solutions Research Articles

Computation of supersonic jet mixing noise for an axisymmetric convergent-divergent nozzle

The turbulent mixing noise of a supersonic jet is calculated for an axisymmetric convergent-divergent nozzle at the design pressure ratio. Aerodynamic computations are performed using the PARC code with a k-e turbulence model. LighthiU's acoustic analogy is adopted. The acoustics solution is based upon the methodology followed in the MGB code. The source correlation function is expressed as a linear combination of second-order tensors (Ribner's assumption). Assuming separable second-order correlations and incorporating Batchelor's isotropic turbulence model, the source term was calculated from the kinetic energy of turbulence. A Gaussian distribution for the time-delay of correlation was introduced. The CFD solution was used to obtain the source strength as well as the characteristic time-delay of correlation. The effect of sound/flow interaction was incorporated using the high frequency asymptotic solution to Lilley's equation for axisymmetric geometries. Acoustic results include sound pressure level directivity and spectra at different polar angles. The aerodynamic and acoustic results demonstrate favorable agreement with experimental data.

An extra-thin light sheet technique used to investigate meniscus shapes by laser induced fluorescence

A light sheet technique is described to accurately (50 μm) measure meniscus profiles in film formation problems. The use of a slit to create the thin (0.1 mm) laser sheet makes the technique easy to implement, and allows tunable sheet thickness. The low light intensity obtained through the slit is compensated by the induced fluorescence of the tested fluid, which provides good picture contrast. After video recording through a microscope, the actual meniscus is recovered by image processing and proper calibration. The efficiency of the technique is demonstrated on a coating flow experiment. Due to its good accuracy and ease of use, this technique is expected to provide useful quantitative information about meniscus problems, in particular for the validation of CFD solutions of coating flows.

An Experimental Study of the Stability of Cantilevered Coaxial Cylindrical Shells Conveying Fluid

This paper presents an experimental study on the stability of a cantilevered cylindrical flexible (silicone rubber) shell, concentrically located within a rigid cylinder and subjected to air flow in either the annular region or inside the shell. Measurements were made of (i) the critical flow velocities of the shell for various (shell length)/radius and (annular gap)/radius ratios, and (ii) frequencies of oscillation of the shell at different subcritical flow velocities. In the case of annular flow, both divergence and flutter were observed, while only flutter was observed for internal flow. The experimental results were compared with those obtained with the two theoretical models previously developed by the authors; in the first, the unsteady shell-motion-induced fluid forces are evaluated by inviscid flow theory, while the steady ones by viscous flow theory (this model is called "Theory 1" for short); in the second, both are calculated by viscous flow theory, with the unsteady forces being obtained from a CFD solution of the linearized, unsteady Navier-Stokes equations (this model is termed "Theory 2"). Theory 1 agrees quantitatively reasonably well with experimental data for annular flow, both in terms of frequencies of oscillation and critical flow velocities, although experimental values of the critical flow velocities are somewhat lower than the theoretical ones; on the other hand, the critical flow velocities as predicted by Theory 2 were found to agree with experimental data far better, in fact extremely well. In case of internal flow, critical flow velocities predicted by Theory 1 are higher than experimental values, but still in fairly good agreement with them.

Airfoil Shape Optimization Using Sensitivity Analysis on Viscous Flow Equations

An aerodynamic shape optimization method has previously been developed by the authors using the Euler equations and has been applied to supersonic-hypersonic nozzle designs. This method has also included a flowfield extrapolation (or flow prediction) method based on the Taylor series expansion of an existing CFD solution. The present paper reports on the extension of this method to the thin-layer Navier-Stokes equations in order to account for the viscous effects. Also, to test the method under highly nonlinear conditions, it has been applied to the transonic flows. Initially, the success of the flow prediction method is tested. Then, the overall method is demonstrated by optimizing the shapes of two supercritical transonic airfoils at zero angle of attack. The first one is shape optimized to achieve a minimum drag while obtaining a lift above a specified value. Whereas, the second one is shape optimized for a maximum lift while attaining a drag below a specified value. The results of these two cases indicate that the present method can produce successfully optimized aerodynamic shapes.

Rotordynamic Coefficients of Multistepped Annular Seals

The basic equations are derived for incompressible flow in multi-stepped annual seals. A 2-D CFD solution is used to verify the model. Exit and entrance loss factors substituted into the bulk flow solution for pressures in the cavity match the 2-D CFD solution. The flow is assumed to be completely turbulent in the axial and circumferential directions with no separation and is modeled using Moody's friction factor relationship. Linearized zeroth- and first-order perturbation equations are developed for small motion about an arbitrary position by an expansion in the eccentricity ratio. The zeroth-order continuity and momentum equations are integrated, yielding the axial and circumferential velocity components and the pressure distribution. The first-order equations are integrated to satisfy the boundary conditions and yield the perturbation pressure distribution. This resultant pressure distribution is integrated along and around the seal to yield the force developed by the seal and the corresponding dynami...

Sources of error in the graphical analysis of CFD results

Graphical techniques are widely used to analyze CFD solutions. Some of these techniques have inherent errors, making them represent the solution imprecisely. An understanding of these errors is important for proper interpretation of the computed results and for comparison with experiments. Examples include contouring, plotting of vector fields, particle tracing, and computation of flow functions involving integration or differentiation.