Study On Rayleigh Taylor Surface Wave Stability Of Planar Liquid Film Based On Spatial Model

This article focuses on the Rayleigh-Taylor(R-T)instability in a planar liquid film and establishes a physical model using spatial modes to study its stability characteristics.The physical model considers small perturbations of surface waves in a compressible composite gas flow induced by a viscous planar jet.The corresponding mathematical model is established by continuity and momentum conservation equations,as well as kinematic boundary conditions.By removing small perturbation terms and linearizing the mathematical model,and considering dynamic boundary conditions,a dimensional dispersion relationship under spatial modes is derived.The paper is based on the Mathematical software and uses the Newton iteration method to program and solve the dispersion relationship derived.The planar liquid film Rayleigh(R)wave and Taylor(T)wave under temporal and spatial modes are compared for downstream and transverse airflow conditions.By changing the dimensionless parameters such as the gasliquid velocity ratio(U,W)on both sides of the liquid film,the liquid Weber numberWel,Reynolds number R el,Euler numberEul,and airflow Mach number Magj,the relationship between the surface wave growth rate ωr,-ki and the longitudinal and transverse wave numbers kx,ky is calculated.The stability of the planar liquid film R-T wave under spatial and temporal modes is analyzed.The study found that:(1)there is little difference in the numerical kx/kr values of the surface wave wr/-ki stability characteristics between temporal and spatial modes,and their variation trends are almost the same,indicating that the spatial and temporal modes are basically consistent within the scope of this study;(2)for the spatial mode Rayleigh wave under downstream or transverse airflow conditions,the surface wave growth rate wr/-ki increases first and then decreases with the increase of wave number kx/kr,until it reaches 0,there exists a dominant surface wave growth rate wr,dom and the corresponding dominant wave number kdom.For the spatial mode Taylor wave under downstream or transverse airflow conditions,the surface wave growth rate decreases with the increase of wave number until it reaches 0.(3)Under both downstream and transverse airflow conditions,as the wave number kx/kr increases,the wavelength of the planar liquid film perturbation at the nozzle exit decreases along the R-wave direction of the jet until it reaches the point of maximum surface wave growth rate wr/-ki,where the most unstable wave number may cause jet fragmentation.Along the T-wave direction perpendicular to the jet injection direction,the surface wave growth rate always decreases with the increase of wave number in the presence of longitudinal wave numbers.(4)The dimensionless parameters such as the gas-liquid velocity ratio U,W on both sides,the liquid Weber number Wel,Reynolds number Rel,Euler number Eul,and airflow Mach number Magj are the most influential factors on jet stability,surface wave growth rate on the spatial axis increases with the increase of these parameters.Finally,regarding the experimental images of planar jet flows from foreign scholar Ippei,numerical calculations were performed under different operating conditions(including different working fluids,momentum ratios MFR,and temperatures)to obtain the relationship between the surface wave growth rate wr and the longitudinal and transverse wave numbers kx,ky in the spatial mode.At the same time,the dominant wave numbers obtained from theoretical calculations were compared with those obtained from experiments,and good agreement was found between the two.Finally,theoretical analysis was carried out using the dispersion relation for the experimental conditions,and it was found that under the condition of downstream airflow,the T-wave waveform appears as a quadratic function for small longitudinal wave numbers kx,while as the longitudinal wave number kx increases,the Twave growth rate shows a decreasing trend.