Jang-Chang Lee

Transonic flow of moist air around a thin airfoil with non-equilibrium and homogeneous condensation

A new small-disturbance model for a steady transonic flow of moist air with non-equilibrium and homogeneous condensation around a thin airfoil is presented. The model explores the nonlinear interactions among the near-sonic speed of the flow, the small thickness ratio and angle of attack of the airfoil, and the small amount of water vapour in the air. The condensation rate is calculated according to classical nucleation and droplet growth models. The asymptotic analysis gives the similarity parameters that govern the flow problem. Also, the flow field can be described by a non-homogeneous (extended) transonic small-disturbance (TSD) equation coupled with a set of four ordinary differential equations for the calculation of the condensate (or sublimate) mass fraction. An iterative numerical scheme which combines Murman & Coles method for the solution of the TSD equation with Simpsons integration rule for the estimation of the condensate mass production is developed. The results show good agreement with available numerical simulations using the inviscid fluid flow equations. The model is used to study the effects of humidity and of energy supply from condensation on the aerodynamic performance of airfoils

Parametric investigation of nonadiabatic compressible flow around airfoils

The compressible flow of a mixture of dry air (an inert carrier gas) and water vapor with nonequilibrium and homogeneous condensation around thin airfoils is examined. The investigation is based on a recent transonic small-disturbance (TSD) theory. The theory provides the governing similarity parameters of the flow and condensation process. The parameters give the relationship between the flow properties, the amount of water vapor mass in the air, and the airfoil’s chord and thickness ratio. The results of varying the similarity parameters are demonstrated by numerical simulations. It is found that heat addition as a result of condensation causes significant changes in the compressible flow behavior and affects the aerodynamic performance of airfoils. Increasing the free-stream frozen Mach number or the airfoil’s chord (with fixed free-stream temperature, pressure, and amount of water vapor) augments the condensation region and the amount of heat transfer to the flow. The heat transfer to the flow also re...

Transonic Flow of Moist Air Around a Thin Airfoil with Equilibrium Condensation

The two-dimensional and steady transonic e ow of atmospheric moist air with equilibrium condensation around a thin airfoil is investigated. The study is based on an asymptotic analysis and numerical simulations. A smalldisturbance model is developed to explore the nonlinear interactions between the near-sonic speed of the e ow, the small thickness ratio and angle of attack of the airfoil, and the small amount of mass of water vapor in the air. The condensation process of water vapor in the air is assumed to be isentropic. The similarity parameters that govern the e ow problem are provided. The e owe eld may be described by a modie ed transonic small-disturbance (TSD)equation that includes parameters that are related to the condensation process. Murman and Cole’ smethod (Murman, E. M., and Cole, J. D., “ Calculation of Plane Study Transonic Flows,” AIAA Journal , Vol. 9, No. 1, 1971, pp. 114 ‐121.)is used for the numerical solution of the modie ed TSD problem. The results show that the e ow of moist air is similar to the e ow of dry air with an effective freestream Mach number that is greater than the freestream Mach number of moist air. The present approach is used to study the aerodynamic performances of airfoils in atmospheric transonic e ight with humidity.

A small-disturbance model of transonic combustion

A new small-disturbance model for a steady, lean, premixed combustion at transonic speeds in a channel of slightly varying area is presented. Attention is confined to dilute premixtures so that exothermicity is weak. The study uses a distinguished limit type of analysis where the nonlinear interactions between (i) the near-sonic speed of the flow, (ii) the small changes in geometry from a straight channel, and (iii) the small heat release due to the one-step first-order Arrhenius chemical reaction, are explored. The asymptotic analysis results in the similarity parameters that govern the reacting flow field. Also, the flow can be described by a nonhomogeneous (extended) transonic small-disturbance (TSD) equation which is coupled with an ordinary differential equation for the calculation of the reactant mass fraction in the combustible gas. An iterative numerical scheme which combines the Murman and Cole method for the solution of the TSD equation with Simpsons integration rule for the estimation of the reactant mass fraction is developed. It is demonstrated that steady-state solutions of the compressible reacting flow problem with detonations behind shock waves can be found. The model is used to study transonic combustion at various inlet Mach numbers, amounts of incoming reactant mass, reaction rates, and channel geometries.

Numerical studies of transonic flow of moist air around a thin airfoil

Numerical studies of a two-dimensional, steady, diabatic transonic flow of a moist air around a thin airfoil are presented. The computations are guided by a recent transonic small-disturbance (TSD) theory of Rusak and Lee14 on this topic. The asymptotic model provides a simplified framework to investigate the changes in the flow field caused by the heat addition from a non-equilibrium process of condensation of the water vapor in the air by homogeneous nucleation. An iterative method which is based on a type-sensitive difference scheme is applied to solve the governing equations. The results demonstrate that the TSD solutions of moist air flows represent the essence of the flow character computed from the inviscid fluid flow equations. Furthermore, guided by the asymptotic relations, the computational results demonstrate the similarity rules for transonic flow of moist air and the effects of energy supply by condensation on the flow behavior.