Numerical Research On Transcritical Flowing Problem

Under the severe pressure environment which higher than the critical point,transcritical flowing phenomenon happens when the fluid flows from low temperature region to high temperature district,and the corresponding fluid thermodynamic state is so called transcritical state.Observed in many important industrial fields,for instance,chemical extraction,heat transfer cooling,aerospace applications and so on,transcritical fluids reveal some strange characteristics that are different from the fluids in normal environment,like the similar density with liquid phase,coincident viscid with gas phase,etc.Therefore,transcritical flowing problem is getting massive attention from researchers because of the potential application value behind it.In this paper the related researches on fuel's transcritical flow problem of rocket engine and scramjet engine in aerospace area are introduced and concluded,meanwhile discussion on its research aspects,study significance and application prospect are made.Base on nitrogen,the PR cubic state equation is used to evaluate the thermodynamic variables in different conditions of pressure and temperature.Variation curves are plotted to conclude the flowing properties of nitrogen and general characteristics of transcritical fluid.Formula derivation is made to demonstrate that the conditional simulation method is failure in solving transcritical problem,meanwhile the mechanics of spurious pressure oscillation are analyzed and the handling strategy is supposed.The double flux model that is widely used in this research is introduced,furthermore,computational program is written base on this method to test several one-dimensional transcritical examples.the conception of uniformed specific heat ratio is put forward and the specific heat ratio fixed method based on one order upwind numerical scheme is designed to remove the pressure oscillation that is reported in transcritical flowing process.Research on high accuracy upwind scheme is made,including the introduction of some popular high order computational methods and result comparison between high order schemes and some primary one order upwind schemes by solving one dimensional shock tube problem.After that a standard five order TENO scheme is used to solve complex supersonic flowing problems to verify the advantage,the application value and the significance of high order computational method.The specific heat ratio fixed method is used to solve two dimensional transcritical nitrogen injection problem and nitrogen/oxygen mixed injection problem in conjunction with Five order TENO scheme and k-? turbulent model,after which the result of double-flux model method that is reported in reference and the result of specific heat ratio fixed method are compared to validate the effect of the new method.Field contours of variation indicate that the specific heat ratio method successfully simulates the two dimensional problem,and the computational result is coincident with images in other papers.On conclusion,a conservative numerical method for transcritical flowing problem is built in this paper and it is successfully used in solving one-dimensional and two-dimensional examples.High order simulation for transcritical flowing problem is realized and related research on flowing structure is made,and the conclusion from this research is able to support the design work of combustion structure of heavy rocket engine and scramjet engine.