Modeling And Analysis On Vibration Behavior Of A Graphite Tube With An Internal Vapor-liquid-solid Flow

Vapor-liquid-solid fluidized bed evaporator that has the properties of anti-scaling and intensification of boiling heat transfer has been applied in many areas,such as salt brine evaporation,traditional Chinese medicine,chemical wastewater pretreatment,etc.However,in order to obtain basic guidance for the optimization design and safe operation in the application of the process composing of the crisp graphite heat tubes,the study of the effect of flow boiling on tube vibration in the heat exchangers is necessary.The main novelties obtained from our study can be listed below.Equations of motion for a straight graphite tube with an internal vapor-liquid-solid flow were derived on the base of Hamilton theory and fluid mechanics.In the established mathematical model,a model of “mixed phase flow” was used to deal with vapor-liquid-solid fluid parameters.The Galerkin method was used to discretize and linearize the equations.The Modality method was used to solve the natural frequency of the tube which was finished by the MATLAB software.Newton difference method was used to analyze parameter sensitivity of the model.The Mathematical Wolfram software was used to verify the process of model derivation and the effect of flow parameters on the tube vibration was also investigated.Numerical calculations indicate that under solid holdup of 1.0% and average glass bead diameter of 2.4 mm,the critical flow velocity is 0.81 m/s.Divergence motion appears when the flow velocity is from 0.81 to 1.15 m/s.The coupled mode flutter occurs when flow velocity is above 1.15 m/s.Parameter sensitivity analysis of the model shows that length of the tube has the most significant impact on the natural frequency of the tube.The natural frequency increases with the increase of void fraction,and decreases with the increase of solid holdup.To study the vibration behavior of the tube subjected to multiphase flow,an experimental program was also carried out.Time series such as vibration acceleration signals in middle of the heat tube with vapor-liquid-solid flow boiling were obtained and time domain and frequency domain analyses were carried out,combining with the pressure data the natural frequency of the tube and the fluid fluctuation frequencies were performed.Experimental results indicate that the addition of solid particles enlarges the amplitude of the vibration acceleration at the same heating steam pressure due to the collision of solid particles with tube walls.The addition of solid particles has little influence on the natural frequencies of the graphite tube,which is in agreement with the model calculation results.The vibration frequency of the fluid was obtained by the analysis of the pressure drop data.Model calculation shows that the resonance of tube subjected to fluid vibration would occur if flow velocity is 0.8 m/s.Nonlinear vibration behavior of reconstructed vibration acceleration signal in multi-phase boiling flow system was discussed at varied solid holdup and steam pressure.(1)The time delay values with minimum points in the correlation integral curves of the reconstructed signals are the same,and are little affected by the solid holdup and the heating steam pressure.(2)The attractor size of the vibration acceleration and the pressure drop signals increases gradually with the increase of solid holdup and heating steam pressure.The influence degree of solid particles on the size of attractor is larger than that of the heating steam pressure.(3)With the increase of the solid holdup,the direction shift of the correlation integral curves was towards to the increase of the super sphere radius r for the complexity of the system increases,and the regularity of the motion decreases.The influence of solid particles on the correlation and regularity of the motion of the system is more obvious than that of steam pressure.(4)Three-scales were obtained namely the macro-scale(motivated by the low frequency behavior of the whole tube vibration or the circulating liquid flow),meso-scale(motivated by intermediate frequency behavior of large vapor bubbles)and the micro-scale(motivated by high frequency behavior of solid particles or small vapor bubbles),respectively.The results of the work can provide the basic theory to guide the design,the operation and the control of vapor-liquid-solid fluidized bed evaporator.