Theory And Application Of Variable-Density Mixing Enhancement Mechanism Under Compressing/Swirling Flows

In the air-breathing power system,a well mixing status is the basis for stable and complete combustion,which determines combustion efficiency,flameout boundary,and emission characteristics.However,in the two rep-resentative advanced powers of ramjet and aeroengine,there are three im-portant challenges to achieve good mixing in the combustion chamber:1.The strong compression environment brought about by ramjet pursuit of higher speed(Mach number（6>1）,leads to the limitation of growth of mixing layer,and the sharp drop in mixing efficiency;2.The pursuit of higher thrust requires the use of high fuel-air ratio and strong swirl com-bustion（swirl number>1）.Facing insufficient mixing,emissions will increase.However,strong mixing causes flameout in lean fuel conditions.3.The combustion process causes significant changes in flow field pressure,temperature,and density,which leads to the traditional constant-density passive-scalar mixing theory invalid,and the mixing enhancement mecha-nism for wide-range density ratio urgently needs to be studied(density ratio=10^-1～10¹).Therefore,this paper extracts the key physical charac-teristics of the strong compression of the ramjet and the strong swirl of the aeroengine,i.e.,the common basic flow structures–a compressible vortex pair with variable-density mixing,and develops the variable-density mixing enhancement mechanisms under the condition of strong compression/strong swirl.The specific research contents are as follows:This paper focuses on the study of compressible vortex pair with variable-density mixing in shock-bubble interaction.First,an equivalent density replacement method is proposed based on numerical simulation,which breaks through the problem of uncontrollable dimensionless num-bers caused by traditional density change methods,and realizes a wide range of density ratio alteration（=0.1～4.0）.Based on this innovative method,it can be found that,compared with the traditional constant-density passive-scalar mixing,the variable-density flow produces a new secondary baroclinic structure,and there is a phenomenon of accelerated decay of the mixed concentration.At the theoretical level,this paper deduces an objective variable-density mixing rate expression for the first time based on the multi-component transport equation,and further reveals the acceleration mecha-nism of the secondary baroclinic structures on the variable-density mixing rate.By establishing a characteristic time theoretical model,dimensionless mixing enhancement number is proposed,and the variable-density mixing enhancement mechanism is verified and validated in two types of flow vortex problems of strong compression(（6=2）and strong swirl（=0～2.3）.This work has the following innovations:Innovation 1:Propose an objective variable-density mixing rate ex-pressionThe hyperbolic non-conservative property of the convection-diffusion equation is deduced for the first time from the unsteady variable-density mul-ticomponent transport equation,and then an objective variable-density mix-ing rate expression is obtained.The expression shows that,compared to the prevailing constant-density passive-scalar mixing,the low-concentration re-gion will experience a concentration decay at a mixing rate up to nearly 7times higher in a variable-density flow,resulting in an anomalous decrease in the mean concentration.Innovation point 2:Reveal the mixing enhancement mechanism of variable-density secondary baroclinic accelerated stretchingThe acceleration mechanism of the local mixing rate by the unsteady variable-density flow structure dominated by the secondary baroclinic vor-tex structure is revealed.By combining the vorticity transport equation and the local mixing convection-diffusion equation,a theoretical model of mix-ing characteristic time for secondary baroclinic vortex-accelerated stretching is established.The model exhibits a variable-density mixing decay charac-teristic time falling at a scaling rate of（1+3/2|⁺|）^-2/3,where the Atwood number reflects the density ratio relationship⁺=（-1）/（+1）.Innovation point 3:Establish the theory of variable-density mixing enhancementBased on the mixing characteristic time model,the dimensionless mix-ing enhancement number?_{（7）≡?*8}/₈^*)is proposed,which compares with the constant-density passive-scalar mixing characteristic time₈^*),the variable-density secondary baroclinic vorticity has a significant effect on the mixing characteristic time_?*₈).Using the mixing enhancement number,aim-ing at the strong compression and strong swirling flow vortex mixing en-hancement,the mixing length is used as the core index to judge the mixing enhancement caused by the density effect,thus preliminarily verifying and applying the variable-density mixing enhancement theory.The basic theoretical research in this paper reveals the unsteady com-pressible single vortex mixing mechanism with a wide range of density al-terations,establishes the variable-density mixing enhancement theory,and provides theoretical support for the future strong compression environment of ramjet combustion and mixing enhancement of strong swirl organization in gas turbine combustors.