Measurement And Calculation Of Shock Stand-off Distance For Spheres Under Mars Entry Condition In Ballistic Ranges

High temperature gas dynamics in CO₂ under mars entry condition gradually becomes one of the focuses of theoretical,numerical and experimental research on hypersonic aerodynamics with the increase of the importancy of mars exploration.Shock stand-off distances for spheres in CO₂ can provide effective validation for related researches.Previous ballistic range experiments of shock stand-off distances for spheres were mainly performed in air with flight speed from 2.5 km/s to 4.0 km/s,data of higher speed are relatively insufficient.Further improvement and validation of engineering and numerical calculation methods of shock stand-off distances for spheres are also needed.To validate the reliability of measurement of shock stand-off distances for hypersonic spheres in ballistic range and acquire accurate experiment data for improvement of engineering methods and validation of numerical calculations,ballistic range experiments of shock stand-off distances for spheres in air and CO₂ have been conducted,respectively.Experiment data of shock stand-off distances for spheres on conditions of flight speeds above 5 km/s in air and simulative flight speeds and ?R states of mars entry trajectory in CO₂ are obtained.Engineering methods of shock stand-off distances for spheres are developed,and calculation accuracy of Park's two temperature model for shock stand-off distances for spheres are validated.The present paper contains six chapters below.Chapter 1 is the introduction.Basic situations of mars explorations both at home and abroad are presented.The review of current theoretical,numerical and experimental researches of shock stand-off distances are made.Existing problems of present researches are summarized and main work of this paper is put forward.Chapter 2 describes the methods of ballistic range experiment of shock stand-off distances for hypersonic spheres.Working principles,equipments arrangement,technical index and measurement methods of hypervelocity ballistic range of China Aerodynamic Research and Development Center are introduced in particulars.Chapter 3 presents the ballistic range experiments of shock stand-off distances for spheres in air.Experimental states in air were designed according to the speed and ?R states of previous study.14 shots with effective experimental data with flight speed above 5 km/s were obtained in caese that ambient pressure from 1.500 kPa to 6.310 kPa and flight speeds from 5.080 km/s to 6.490 km/s.1 shot with effective experimental data with flight speeds from 2.5 km/s to 4.0 km/s was obtained with ambient pressure of 4.200 kPa and flight speed of 2.690 km/s.Results show the measurement methods are reliable,and the data are comparable with the data obtained from other facilities.Shadowgraph is find to be more beneficial for shock stand-off distance measurement.According to numerical results,the flow near the stagnation points of spheres in air with flight speeds above 5 km/s of present experiment are speculated to be basically nonequilibrium and gradually becomes frozen as ?R increases.Shock stand-off distances for spheres with flight speeds above 5 km/s increase as ?R increases,which is in contrary to the trend that shock stand-off distances changing with ?R with flight speeds from 2.5 km/s to 4.0 km/s.It is inferred that pR influences the flow state near the stagnation points of spheres differently with different speeds.Engineering method of predicting shock stand-off distances for spheres in air was improved based on the present experiment data.The differences between the predicted data using improved method and the measured data are within ±20%,while the original method can not predict the experimental results.Chapter 4 describes the ballistic experiments of shock stand-off distances for spheres in CO₂.Experimental conditions in CO₂ were designed according to the speeds and pR states at different heights?25 km,30 km,35 km and 40 km?of a typical mars entry trajectory.Replacement method of test gas in test section was proposed.One shot with effective experimental data in CO₂ was obtained for each selected height,with ambient pressures from 2.420 kPa to 12.300 kPa and flight speeds from 2.122 km/s to 4.220 km/s.Comparable experiment in air with same pressures and speeds have been performed,too.Results show the shadowgraph can obtain shock stand-off distances in CO₂ for cases above.High temperature gas effect is more obvious in CO₂ than in air on conditions of the same pressure and speed,and there would be a certain correlation between the data measured in CO₂ and in air.According to numerical results,the flow near the stagnation points of spheres in CO₂ are supposed to be basically nonequilibrium.Engineering method of predicting shock stand-off distances for spheres in CO₂ is established based on the present measured data.Predicted shock stand-off distances generally agree with measured data.However,the influence of different ?R has on shock stand-off distance needs to be further studied.Chapter 5 analyzes numerical calculations of shock stand-off distances for hypersonic spheres.Calculation methods of flow field both in air and CO₂ with perfect,equilibrium,frozen and Park's two temperature nonequilibrium models are presented.Calculation results are compared with experiment data in Chapter 3 and 4 and data in references to validate the accuracy of two temperature nonequilibrium model when calculating the shock stand-off distances for spheres in air with flight speeds above 5 km/s and in CO₂.Results show the two temperature nonequilibrium model predicts experimental data well.It is indicated that for present experiments the flow near stagnation points of spheres in air with flight speed above 5 km/s of are basically nonequilibrium and gradually approach equilibrium downstream,and the flow from upstream to downstream of spheres in CO₂ are primarily nonequilibrium.Chapter 6 is the conclusion.Main works and conclusions of this paper are given.Three problems are put forward for further investigation.