A computational method for viscous incompressible flows

An implicit, finite-difference procedure for numerically solving viscous incompressible flows is presented. The pressure-field solution is based on the pseudocompressibility method in which a time-derivative pressure term is introduced into the mass-conservation equation to form a set of hyperbolic equations. The pressure-wave propagation and the spreading of the viscous effect is investigated using simple test problems. Computed results for external and internal flows are presented to verify the present method which has proved to be very robust in simulating incompressible flows

Gas flows through shallow T-junctions and parallel microchannel networks

We apply a recent extension of the Hele-Shaw scheme to analyze steady compressible viscous flows through micro T-junctions. The linearity of the problem in terms of an appropriately defined quadratic form of the pressure facilitates the definition of the viscous resistance of the configuration, relating the gas mass-flow rate to entrance and exit conditions. Furthermore, under rather mild restrictions, the performance of complex microchannel networks may be estimated through superposition of the contributions of multiple basic junction elements. This procedure is applied to an optimization model problem of a parallel microchannel network. The analysis and results are readily adaptable to incompressible flows

Numerical approach for the aerodynamic analysis if airfoils with laminar separation

A numerical method for simultaneously and efficiently coupling an external subsonic potential flow and an interior viscous flow such that the two flows match at an interfacing boundary is discussed. Both a panel method and a simple point compressible vortex model are used for the outer potential field. The interior flow solvers which were used are the Navier-Stokes and Euler codes of T. J. Coakley and the Euler code of A. Verhoff. In order to test compatibility, the panel method is coupled to the less expensive Euler codes since the coupling procedure is identical with the Navier-Stokes code. The results show significant efficiency improvements can be obtained over the uncoupled approach. Results also indicate the outer potential flow is best represented by the simple point compressible vortex model. The panel method couples smoothly to Coakley's implicit code but is numerically incompatible as coupled with the explicit Euler code. An improved Navier-Stokes code is under initial development which extends the Euler code to include the necessary viscous terms. Results are shown for all infinite length channel with one wavy periodic wall with and without laminar separation

A compressible Navier-Stokes code for turbulent flow modeling

An implicit, finite volume code for solving two dimensional, compressible turbulent flows is described. Second order upwind differencing of the inviscid terms of the equations is used to enhance stability and accuracy. A diagonal form of the implicit algorithm is used to improve efficiency. Several zero and two equation turbulence models are incorporated to study their impact on overall flow modeling accuracy. Applications to external and internal flows are discussed

Nonmodal energy growth and optimal perturbations in compressible plane Couette flow

Nonmodal transient growth studies and estimation of optimal perturbations have been made for the compressible plane Couette flow with three-dimensional disturbances. The maximum amplification of perturbation energy over time, $G_{\max}$, is found to increase with increasing Reynolds number ${\it Re}$, but decreases with increasing Mach number $M$. More specifically, the optimal energy amplification $G_{\rm opt}$ (the supremum of $G_{\max}$ over both the streamwise and spanwise wavenumbers) is maximum in the incompressible limit and decreases monotonically as $M$ increases. The corresponding optimal streamwise wavenumber, $\alpha_{\rm opt}$, is non-zero at M=0, increases with increasing $M$, reaching a maximum for some value of $M$ and then decreases, eventually becoming zero at high Mach numbers. While the pure streamwise vortices are the optimal patterns at high Mach numbers, the modulated streamwise vortices are the optimal patterns for low-to-moderate values of the Mach number. Unlike in incompressible shear flows, the streamwise-independent modes in the present flow do not follow the scaling law $G(t/{\it Re}) \sim {\it Re}^2$, the reasons for which are shown to be tied to the dominance of some terms in the linear stability operator. Based on a detailed nonmodal energy analysis, we show that the transient energy growth occurs due to the transfer of energy from the mean flow to perturbations via an inviscid {\it algebraic} instability. The decrease of transient growth with increasing Mach number is also shown to be tied to the decrease in the energy transferred from the mean flow ($\dot{\mathcal E}_1$) in the same limit