Discharge Coefficient Of Sonic Nozzle Based On Surface Structure And Thermal Effect

In many fields such as energy conservation and emission reduction,safety monitoring,national defense and military project,and scientific research,the gas flow measurement plays an important role.The accuracy flow measurement is able to guarantee the realiability of application.Sonic nozzles usually are used as a flowmeter to measure the gas flow or used as the master meter in the secondary standard to calibrate other kinds of flowmeters,due to its simple structure and stable metering performance.In this study,the sonic nozzle was taken as the research object,focusing on the discharge coefficient,which is the most significant metrological performance parameter.Mainly through theoretical analysis,numerical simulation and experimental measurement,a method for calculating discharge coefficient was proposed based on the measurement of macroscopic surface structure parameters,which does not need to be calibrated by experiments.Then,the constraint conditions of this method were determined by using the relative maximum roughness as the evaluation parameter to analyze the boundary layer transition and turbulence characteristics.Finally,the influence of temperature drop condensation and fluid solid thermal coupling phenomenon on the metrological characteristics of sonic nozzle was studied,which effectively improved the accuracy of the calculation method for discharge coefficient under complex working conditions.The main results and conclusions are as following:1)According to the theoretical formula and experimental results of discharge coefficient,the key characteristic parameters were proposed,and the variation characteristics between the discharge coefficient and the Reynolds number at throat in different boundary layer regions were clarified.Based on the inviscid discharge coefficient in the multi-dimensional core region and the viscous discharge coefficient in the boundary layer region,a formula of discharge coefficient for non-adiabatic wall conditions in laminar boundary layer were established to extract the key characteristic parameters of surface structure and thermal effect.The p VTt gas flow standard facility with the expanded uncertainty of(0.08 ～ 0.10)%(k = 2)was established by accurately controlling of the key parameters,such as intaking time,additional mass and leakage,which was verified by international comparison among laboratories.Based on this facility,the values of discharge coefficients of 21 sonic nozzles with different throat diameters were obtained experimentally.The results revealed that the variation of the discharge coefficient with the throat Reynolds number covering the whole boundary layers.It provides theoretical support and technical basis for the study of the surface structure and flow and heat transfer characteristics of sonic nozzle.2)A method of discharge coefficient without real flow calibration based on the measurement of the macroscopic surface structure parameters of sonic nozzle were proposed.The macro surface structure of sonic nozzles were measured by using 3D coordinate measuring machine.The detailed measurement procedures and evaluation criteria of the throat diameter,curvature radius,roundness and waviness were presented taking into account both measurement efficiency and accuracy.The effective throat diameter and curvature radius would be obtained when the surface structure of sonic nozzle meets the requirements of the evaluation criteria and measurement procedures.Furthermore,with combination of the stagnation temperature,pressure and physical parameters of gas,the discharge coefficient in the laminar boundary layer were accurately obtained by using this method,and its accuracy would reach 0.11%.The accuracy and reliability of this method were verified by experimental data.This method significantly improves the accuracy of the discharge coefficient in the case of small Reynolds number and curvature radius.3)The constraint conditions of this method for discharge coefficient were determined by using the relative maximum roughness as the evaluation parameter and analyzing the boundary layer transition and turbulence characteristics.The parameters of meso-micro surface structure for sonic nozzles with different throat diameters were extracted by using high precision surface roughness instrument(HPSRI).It is pointed out that the maximum surface roughness can be used as an assessment criteria to evaluate the equivalent roughness.At the same time,based on the SST(Shear-Stress Transport)transition model,the development and transition mechanism of boundary layer under different relative equivalent roughness were conducted to further obtained the beginning and ending positions of boundary layer transition.The inverse relationship between the relative equivalent roughness and the beginning Reynolds number of the transition of boundary layer at throat was established.Then,the constraint conditions of the method for discharge coefficient would be determined.Moreover,the effect of waviness profile on the displacement boundary layer thickness of sonic nozzle was investigated quantitatively for the first time,which further completes the meso-micro surface structure parameters.4)The influence of temperature drop condensation and fluid solid thermal coupling phenomenon on the metrological characteristics of sonic nozzle was clarified in detail.The typical pressure characteristics of condensation phenomenon through ISO and non-ISO sonic nozzle under different stagnation conditions were captured to explore the variation of conditions,position,pressure oscillation frequency and intensity,and boundary layer displacement thickness of condensation,by using a multi-parameter adjustable humidification apparatus,pressure sensor array and data processing methods.Then,the temperature fields of sonic nozzle solid domain were reconstructed and visualized by using the thermocouple temperature sensor array system,non-adiabatic boundary layer equation similarity solution and unsteady fluid solid thermal coupling model,and the improved interpolation algorithm.Based on the reconstructed wall temperature distribution,the influence of thermal boundary layer and constrained thermal deformation on the discharge coefficient was quantified,which effectively improves the accuracy of the calculation method for discharge coefficient under complex working conditions,and further broadens its application range under small Reynolds number.