In this work, a magnetic fluid dynamics （MHD） model is used to simulate the electromagnetic field, heat transfer and fluid flow in a DC non-transferred arc plasma torch under laminar and turbulent conditions. The el...In this work, a magnetic fluid dynamics （MHD） model is used to simulate the electromagnetic field, heat transfer and fluid flow in a DC non-transferred arc plasma torch under laminar and turbulent conditions. The electric current density, temperature and velocity distributions in the torch are obtained through the coupled iterative calculation about the electromagnetic equations described in a magnetic vector potential format and the modified fluid dynamics equations. The fluid-solid coupled calculation method is applied to guarantee the continuity of the electric current and heat transfer at the interface between the electrodes and fluid. The predicted location of the anodic arc root attachment and the arc voltage of the torch are consistent with corresponding experimental results. Through a specific analysis of the influence of mass flow rates and electric current on the torch outlet parameters, the total thermal efficiency, thermal loss of each part, and the laws of the variation of outlet parameters with the variation of mass flow rates and electric current was obtained. It is found that operation under a laminar condition with a limited area of the anode could increase the total thermal efficiency of the torch.展开更多
Five turbulence models of Reynolds average Navier-Stokes(RANS),including the standard k-ω model,the RNG k-e model taking into account the low Reynolds number effect,the realizable k-ω model,the SST k-ω model,and th...Five turbulence models of Reynolds average Navier-Stokes(RANS),including the standard k-ω model,the RNG k-e model taking into account the low Reynolds number effect,the realizable k-ω model,the SST k-ω model,and the Reynolds stress model(RSM),are employed in the numerical simulations of direct current(DC)arc plasma torches in the range of arc current from 80 A to 240 A and air gas flow rate from 10 m^3 h^-1 to 50 m^3 h^-1.The calculated voltage,electric field intensity,and the heat loss in the arc chamber are compared with the experiments.The results indicate that the arc voltage,the electric field,and the heat loss in the arc chamber calculated by using the standard k-ω model,the RNG k-ωmodel taking into account the low Reynolds number effect,and the realizable k-ω model are much larger than those in the experiments.The RSM predicts relatively close results to the experiments,but fails in the trend of heat loss varying with the gas flow rate.The calculated results of the SST k-ω model are in the best agreement with the experiments,which may be attributed to the reasonable predictions of the turbulence as well as its distribution.展开更多
A modelling study is performed to investigate the characteristics of both plasma flow and heat transfer of a laminar non-transferred arc argon plasma torch operated at atmospheric and reduced pressure. It is found tha...A modelling study is performed to investigate the characteristics of both plasma flow and heat transfer of a laminar non-transferred arc argon plasma torch operated at atmospheric and reduced pressure. It is found that the calculated flow fields and temperature distributions are quite similar for both cases at a chamber pressure of 1.0 atm and 0.1 atm. A fully developed flow regime could be achieved in the arc constrictor-tube between the cathode and the anode of the plasma torch at 1.0 atm for all the flow rates covered in this study. However the flow field could not reach the fully developed regime at 0.1 atm with a higher flow rate. The arc-root is always attached to the torch anode surface near the upstream end of the anode, i.e. the abruptly expanded part of the torch channel, which is in consistence with experimental observation. The surrounding gas would be entrained from the torch exit into the torch interior due to a comparatively large inner diameter of the anode channel compared to that of the arc constrictor-tube.展开更多
Experimental beneficiation processes of quartz concentrate in arc plasma torches of two different types and electric powers were studied. An emission scanning electron microscope and a universal laser analyzer were us...Experimental beneficiation processes of quartz concentrate in arc plasma torches of two different types and electric powers were studied. An emission scanning electron microscope and a universal laser analyzer were used to investigate the structures as well as the size distributions of grains and microparticles. Inductively coupled plasma–mass spectrometry was used to determine the chemical compositions of nonstructural solid-phase mineral impurities in quartz concentrate. Results related to the modified grains' structure and size distribution, the compositions of impurities, and the gas–liquid inclusions in the quartz concentrate were investigated. The total impurities concentrations in the processed grains were found to satisfy the IOTA-STD standard(industry standard for grading high quality fused quartz products). The optimal condition(i.e., the optimal specific plasma enthalpy) for the production of high-purity quartz in arc plasma torches was found to depend on the geological-genetic type and the structural and textural features(i.e., chemical composition and gas–liquid inclusions) of the quartz concentrate.展开更多
A three-dimensional numerical model is developed to study the behaviour of an argon-nitrogen plasma arc inside a non-transferred torch. In this model, both the entire cathode and anode nozzle are considered to simulat...A three-dimensional numerical model is developed to study the behaviour of an argon-nitrogen plasma arc inside a non-transferred torch. In this model, both the entire cathode and anode nozzle are considered to simulate the plasma arc. The argon-nitrogen plasma arc is simulated for different arc currents and gas flow rates of argon. Various combinations of arc core radius and arc length, which correspond to a given torch power, are predicted. A most feasible combination of the same, which corresponds to an actual physical situation of the arc inside the torch, is identified using the thermodynamic principle of minimum entropy production for a particular torch power. The effect of the arc current and gas flow rate on the plasma arc characteristics and torch efficiency is explained. The effect of the nitrogen content in the plasma gas on the torch power and efficiency is clearly detected. Predicted torch efficiencies are comparable to the measured ones and the effect of the arc current and gas flow rate on predicted and measured efficiencies is almost similar. The efficiency of the torch, cathode and anode losses and core temperature and velocity at the nozzle exit are reported for five different cases.展开更多
In this paper, characteristics of a treatment and operated at atmospheric pressure dual torch plasma arc used for hazardous waste are studied, and also compared with those of the multi-torch plasma arc and the single ...In this paper, characteristics of a treatment and operated at atmospheric pressure dual torch plasma arc used for hazardous waste are studied, and also compared with those of the multi-torch plasma arc and the single torch plasma arc. The dual torch plasma arc is generated between the cathode and anode with argon as the working gas. The temperature distributions of the plasma arc are measured using a spectroscope and line pair method with the assumption of local thermodynamic equilibrium （LTE） for the DC arc current I=100 A and argon flow rate Q = 15 slpm. The measurements show that the temperatures of the dual torch arc plasma in the regions near the cathode, the anode and the center point are 10,000 K, 11,000 K and 9,000 K, respectively. And the high temperature region of the multi torch plasma arc is of double or much wider size than that of a conventional dual torch plasma arc and single plasma torch. Based on the preceding studies, a dual torch plasma arc furnace is developed in this study. The measured gas temperature at the center region of the argon arc is about 11,000 K for the case of I=200 A and Q=30 slpm operated in atmosphere.展开更多
Results observed experimentally are presented, about the DC arc plasma jets and their arc-root behaviour generated at reduced gas pressure without or with an applied magnetic field. Pure argon, argon-hydrogen or argon...Results observed experimentally are presented, about the DC arc plasma jets and their arc-root behaviour generated at reduced gas pressure without or with an applied magnetic field. Pure argon, argon-hydrogen or argon-nitrogen mixture was used as the plasma-forming gas. A specially designed copper mirror was used for a better observation of the arc-root behaviour on the anode surface of the DC non-transferred arc plasma torch. It was found that in the cases without an applied magnetic field, the laminar plasma jets were stable and approximately axisymmetrical. The arc-root attachment on the anode surface was completely diffusive when argon was used as the plasma-forming gas, while the arc-root attachment often became constrictive when hydrogen or nitrogen was added into the argon. As an external magnetic field was applied, the arc root tended to rotate along the anode surface of the non-transferred arc plasma torch.展开更多
Thermal steam plasma jet is promising for applications in environmental industries due to its distinctive characteristics of high enthalpy and high chemical reactivity. However, the performance of the steam plasma tor...Thermal steam plasma jet is promising for applications in environmental industries due to its distinctive characteristics of high enthalpy and high chemical reactivity. However, the performance of the steam plasma torch for its generation is limited by the problems of the large arc voltage fluctuation and serious erosion of the electrodes. In this study, a gas-stabilized steam plasma torch which can operate continuously and stably was designed. Experiments were conducted to reveal the effect of the different working parameters, including the anode diameter, the cooling water temperature, the arc current and the steam flow rate, on its Volt-Ampere characteristics, arc voltage fluctuation, thermal efficiency, jet characteristics and electrodes erosion. Results showed that the use of hot water to cool the electrodes can effectively prevent the condensation of steam on the inner wall of the electrodes, thus significantly reducing the arc voltage fluctuations and electrodes erosion. This is crucial for increasing the working life of the electrodes and ensuring long-term stability of the steam plasma torch. In addition, suitable anode diameter can greatly reduce the arc voltage fluctuation of the steam plasma torch and effectively improve the stability of the steam plasma jet. Furthermore, high arc current can effectively reduce the fluctuations of the arc voltage and increase the length and the volume of the steam plasma jet. Finally, using steam as the plasma forming gas can achieve higher thermal efficiency compared to air. An ideal thermal efficiency can be achieved by properly reducing the arc current and increasing the steam flow rate.展开更多
A water plasma was generated by DC arc discharge with a hafnium embedded rodtype cathode and a nozzle-type anode. The discharge characteristics were examined by changing the operation parameter of the arc current. The...A water plasma was generated by DC arc discharge with a hafnium embedded rodtype cathode and a nozzle-type anode. The discharge characteristics were examined by changing the operation parameter of the arc current. The dynamic behavior of the arc discharge led to significant fluctuations in the arc voltage and its frequency. Analyses of the high speed image and the arc voltage waveform showed that the arc discharge was in the restrike mode and its frequency varied within several tens of kilohertz according to the operating conditions. The larger thermal plasma volume was generated by the higher flow from the forming steam with a higher restrike frequency in the higher arc current conditions. In addition, the characteristics of the water plasma jet were investigated by means of optical emission spectroscopy to identify the abundant radicals required in an efficient waste treatment process.展开更多
In this paper, a low pressure Ar/N2 shock plasma jet with clearly multicycle al- ternating zones produced by a DC cascade arc discharge has been investigated by an emission spectral method combined with Abel inversion...In this paper, a low pressure Ar/N2 shock plasma jet with clearly multicycle al- ternating zones produced by a DC cascade arc discharge has been investigated by an emission spectral method combined with Abel inversion analysis. Plasma emission intensity, electron, vi- brational and rotational temperatures of the shock plasma have been measured in the expansion and compression zones. The results indicate that the ranges of the measured electron temperature, vibrational temperature and rotational temperature are 1.1 eV to 1.6 eV, 0.2 eV to 0.7 eV and 0.19 eV to 0.22 eV, respectively, and it is found for the first time that the vibrational and rota- tional temperatures increase while the electron temperature decreases in the compression zones. The electron temperature departs from the vibrational and the rotational temperatures due to non-equilibrium plasma effects. Electrons and heavy particles could not completely exchange energy via collisions in the shock plasma jet under the low pressure of 620 Pa or so.展开更多
The effect of various process parameters like welding current, torch height, welding speed and plasma gas flow rate on front melting width, back melting width and weld reinforcement of plasma arc welding on aluminum a...The effect of various process parameters like welding current, torch height, welding speed and plasma gas flow rate on front melting width, back melting width and weld reinforcement of plasma arc welding on aluminum alloy is investigated by using factorial design approach. Variable polarity plasma arc welding is used for welding aluminum alloy. Trail experiments are conducted and the limits of the input process parameters are decided. Two levels and four input process parameters are chosen and experiments are conducted as per typical design matrix considering full factorial design. Total sixteen experiments are conducted and output responses are measured. The coefficients are calculated by using regression analysis and the mathematical models are constructed. By using the mathematical models the main and interaction effect of various process parameters on weld quality is studied.展开更多
Modeling results are presented for the laminar flow and heat transfer within a circular tube connected coaxially with a d c arc plasma torch. In order to determine the correct boundary conditions at the tube in...Modeling results are presented for the laminar flow and heat transfer within a circular tube connected coaxially with a d c arc plasma torch. In order to determine the correct boundary conditions at the tube inlet, the computational domain is extended to include both the circular tube and the arc plasma torch. Computational results show that the gas static pressure in the tube increases at first and then decreases slowly, while the heat flux to the tube wall decreases monotonically with increasing distance from the tube inlet. Comparison of some computed results with corresponding experimental data is also given.展开更多
为了更好地研究直流电弧等离子体炬内的流动与传热,根据磁流体动力学(MHD)理论建立了等离子体电弧区的数学物理模型,采用磁矢量势A的方法来计算磁感应强度B的大小,利用通用软件FLUENT并进行二次开发,采用用户自定义函数(user defined fu...为了更好地研究直流电弧等离子体炬内的流动与传热,根据磁流体动力学(MHD)理论建立了等离子体电弧区的数学物理模型,采用磁矢量势A的方法来计算磁感应强度B的大小,利用通用软件FLUENT并进行二次开发,采用用户自定义函数(user defined function,UDF)加入磁流体动力学方程组中的源项和物性参数,并利用用户自定义标量方程(user defined scalar,UDS)的方法加入Maxwell方程组,采用SIMPLE算法对电弧区域进行了数值模拟。计算结果表明:等离子体炬内的弧电压随着气体质量流量的增加而增加;等离子体炬内的温度随着气体质量流量的增加而减小,而速度随着气体质量流量的增加而增加;出口处的温度和速度随径向距离的增加而减小,但温度减小的速率增加。这一结果可为实验提供理论指导和参考。展开更多
基金supported by National Natural Science Foundation of China (No. 50476081)
文摘In this work, a magnetic fluid dynamics （MHD） model is used to simulate the electromagnetic field, heat transfer and fluid flow in a DC non-transferred arc plasma torch under laminar and turbulent conditions. The electric current density, temperature and velocity distributions in the torch are obtained through the coupled iterative calculation about the electromagnetic equations described in a magnetic vector potential format and the modified fluid dynamics equations. The fluid-solid coupled calculation method is applied to guarantee the continuity of the electric current and heat transfer at the interface between the electrodes and fluid. The predicted location of the anodic arc root attachment and the arc voltage of the torch are consistent with corresponding experimental results. Through a specific analysis of the influence of mass flow rates and electric current on the torch outlet parameters, the total thermal efficiency, thermal loss of each part, and the laws of the variation of outlet parameters with the variation of mass flow rates and electric current was obtained. It is found that operation under a laminar condition with a limited area of the anode could increase the total thermal efficiency of the torch.
基金National Natural Science Foundation of China(Nos.11675177,11875256)the Anhui Province Scientific and Technological Project(No.1604a0902145).
文摘Five turbulence models of Reynolds average Navier-Stokes(RANS),including the standard k-ω model,the RNG k-e model taking into account the low Reynolds number effect,the realizable k-ω model,the SST k-ω model,and the Reynolds stress model(RSM),are employed in the numerical simulations of direct current(DC)arc plasma torches in the range of arc current from 80 A to 240 A and air gas flow rate from 10 m^3 h^-1 to 50 m^3 h^-1.The calculated voltage,electric field intensity,and the heat loss in the arc chamber are compared with the experiments.The results indicate that the arc voltage,the electric field,and the heat loss in the arc chamber calculated by using the standard k-ω model,the RNG k-ωmodel taking into account the low Reynolds number effect,and the realizable k-ω model are much larger than those in the experiments.The RSM predicts relatively close results to the experiments,but fails in the trend of heat loss varying with the gas flow rate.The calculated results of the SST k-ω model are in the best agreement with the experiments,which may be attributed to the reasonable predictions of the turbulence as well as its distribution.
基金supported by National Natural Science Foundation of China (Nos. 10575127, 10772016)the Doctoral Research Fund of Higher Education of China (No. 20070006022)
文摘A modelling study is performed to investigate the characteristics of both plasma flow and heat transfer of a laminar non-transferred arc argon plasma torch operated at atmospheric and reduced pressure. It is found that the calculated flow fields and temperature distributions are quite similar for both cases at a chamber pressure of 1.0 atm and 0.1 atm. A fully developed flow regime could be achieved in the arc constrictor-tube between the cathode and the anode of the plasma torch at 1.0 atm for all the flow rates covered in this study. However the flow field could not reach the fully developed regime at 0.1 atm with a higher flow rate. The arc-root is always attached to the torch anode surface near the upstream end of the anode, i.e. the abruptly expanded part of the torch channel, which is in consistence with experimental observation. The surrounding gas would be entrained from the torch exit into the torch interior due to a comparatively large inner diameter of the anode channel compared to that of the arc constrictor-tube.
文摘Experimental beneficiation processes of quartz concentrate in arc plasma torches of two different types and electric powers were studied. An emission scanning electron microscope and a universal laser analyzer were used to investigate the structures as well as the size distributions of grains and microparticles. Inductively coupled plasma–mass spectrometry was used to determine the chemical compositions of nonstructural solid-phase mineral impurities in quartz concentrate. Results related to the modified grains' structure and size distribution, the compositions of impurities, and the gas–liquid inclusions in the quartz concentrate were investigated. The total impurities concentrations in the processed grains were found to satisfy the IOTA-STD standard(industry standard for grading high quality fused quartz products). The optimal condition(i.e., the optimal specific plasma enthalpy) for the production of high-purity quartz in arc plasma torches was found to depend on the geological-genetic type and the structural and textural features(i.e., chemical composition and gas–liquid inclusions) of the quartz concentrate.
文摘A three-dimensional numerical model is developed to study the behaviour of an argon-nitrogen plasma arc inside a non-transferred torch. In this model, both the entire cathode and anode nozzle are considered to simulate the plasma arc. The argon-nitrogen plasma arc is simulated for different arc currents and gas flow rates of argon. Various combinations of arc core radius and arc length, which correspond to a given torch power, are predicted. A most feasible combination of the same, which corresponds to an actual physical situation of the arc inside the torch, is identified using the thermodynamic principle of minimum entropy production for a particular torch power. The effect of the arc current and gas flow rate on the plasma arc characteristics and torch efficiency is explained. The effect of the nitrogen content in the plasma gas on the torch power and efficiency is clearly detected. Predicted torch efficiencies are comparable to the measured ones and the effect of the arc current and gas flow rate on predicted and measured efficiencies is almost similar. The efficiency of the torch, cathode and anode losses and core temperature and velocity at the nozzle exit are reported for five different cases.
文摘In this paper, characteristics of a treatment and operated at atmospheric pressure dual torch plasma arc used for hazardous waste are studied, and also compared with those of the multi-torch plasma arc and the single torch plasma arc. The dual torch plasma arc is generated between the cathode and anode with argon as the working gas. The temperature distributions of the plasma arc are measured using a spectroscope and line pair method with the assumption of local thermodynamic equilibrium （LTE） for the DC arc current I=100 A and argon flow rate Q = 15 slpm. The measurements show that the temperatures of the dual torch arc plasma in the regions near the cathode, the anode and the center point are 10,000 K, 11,000 K and 9,000 K, respectively. And the high temperature region of the multi torch plasma arc is of double or much wider size than that of a conventional dual torch plasma arc and single plasma torch. Based on the preceding studies, a dual torch plasma arc furnace is developed in this study. The measured gas temperature at the center region of the argon arc is about 11,000 K for the case of I=200 A and Q=30 slpm operated in atmosphere.
基金the National Natural Science Foundation of China(Nos.10575127,50336010)
文摘Results observed experimentally are presented, about the DC arc plasma jets and their arc-root behaviour generated at reduced gas pressure without or with an applied magnetic field. Pure argon, argon-hydrogen or argon-nitrogen mixture was used as the plasma-forming gas. A specially designed copper mirror was used for a better observation of the arc-root behaviour on the anode surface of the DC non-transferred arc plasma torch. It was found that in the cases without an applied magnetic field, the laminar plasma jets were stable and approximately axisymmetrical. The arc-root attachment on the anode surface was completely diffusive when argon was used as the plasma-forming gas, while the arc-root attachment often became constrictive when hydrogen or nitrogen was added into the argon. As an external magnetic field was applied, the arc root tended to rotate along the anode surface of the non-transferred arc plasma torch.
基金the support of the Key Research Program of the Sichuan Provincial Science and Technology Department,China(No.2017GZ0096)
文摘Thermal steam plasma jet is promising for applications in environmental industries due to its distinctive characteristics of high enthalpy and high chemical reactivity. However, the performance of the steam plasma torch for its generation is limited by the problems of the large arc voltage fluctuation and serious erosion of the electrodes. In this study, a gas-stabilized steam plasma torch which can operate continuously and stably was designed. Experiments were conducted to reveal the effect of the different working parameters, including the anode diameter, the cooling water temperature, the arc current and the steam flow rate, on its Volt-Ampere characteristics, arc voltage fluctuation, thermal efficiency, jet characteristics and electrodes erosion. Results showed that the use of hot water to cool the electrodes can effectively prevent the condensation of steam on the inner wall of the electrodes, thus significantly reducing the arc voltage fluctuations and electrodes erosion. This is crucial for increasing the working life of the electrodes and ensuring long-term stability of the steam plasma torch. In addition, suitable anode diameter can greatly reduce the arc voltage fluctuation of the steam plasma torch and effectively improve the stability of the steam plasma jet. Furthermore, high arc current can effectively reduce the fluctuations of the arc voltage and increase the length and the volume of the steam plasma jet. Finally, using steam as the plasma forming gas can achieve higher thermal efficiency compared to air. An ideal thermal efficiency can be achieved by properly reducing the arc current and increasing the steam flow rate.
文摘A water plasma was generated by DC arc discharge with a hafnium embedded rodtype cathode and a nozzle-type anode. The discharge characteristics were examined by changing the operation parameter of the arc current. The dynamic behavior of the arc discharge led to significant fluctuations in the arc voltage and its frequency. Analyses of the high speed image and the arc voltage waveform showed that the arc discharge was in the restrike mode and its frequency varied within several tens of kilohertz according to the operating conditions. The larger thermal plasma volume was generated by the higher flow from the forming steam with a higher restrike frequency in the higher arc current conditions. In addition, the characteristics of the water plasma jet were investigated by means of optical emission spectroscopy to identify the abundant radicals required in an efficient waste treatment process.
基金supported by the National Magnetic Confinement Fusion Science Program of China(Nos.2013GB109005,2009GB106004)National Natural Science Foundation of China(Nos.11175035,10875023)the Fundamental Research Funds for the Central Universities of China(DUT 12ZD(G)01,DUT 11ZD(G)06)
文摘In this paper, a low pressure Ar/N2 shock plasma jet with clearly multicycle al- ternating zones produced by a DC cascade arc discharge has been investigated by an emission spectral method combined with Abel inversion analysis. Plasma emission intensity, electron, vi- brational and rotational temperatures of the shock plasma have been measured in the expansion and compression zones. The results indicate that the ranges of the measured electron temperature, vibrational temperature and rotational temperature are 1.1 eV to 1.6 eV, 0.2 eV to 0.7 eV and 0.19 eV to 0.22 eV, respectively, and it is found for the first time that the vibrational and rota- tional temperatures increase while the electron temperature decreases in the compression zones. The electron temperature departs from the vibrational and the rotational temperatures due to non-equilibrium plasma effects. Electrons and heavy particles could not completely exchange energy via collisions in the shock plasma jet under the low pressure of 620 Pa or so.
文摘The effect of various process parameters like welding current, torch height, welding speed and plasma gas flow rate on front melting width, back melting width and weld reinforcement of plasma arc welding on aluminum alloy is investigated by using factorial design approach. Variable polarity plasma arc welding is used for welding aluminum alloy. Trail experiments are conducted and the limits of the input process parameters are decided. Two levels and four input process parameters are chosen and experiments are conducted as per typical design matrix considering full factorial design. Total sixteen experiments are conducted and output responses are measured. The coefficients are calculated by using regression analysis and the mathematical models are constructed. By using the mathematical models the main and interaction effect of various process parameters on weld quality is studied.
文摘Modeling results are presented for the laminar flow and heat transfer within a circular tube connected coaxially with a d c arc plasma torch. In order to determine the correct boundary conditions at the tube inlet, the computational domain is extended to include both the circular tube and the arc plasma torch. Computational results show that the gas static pressure in the tube increases at first and then decreases slowly, while the heat flux to the tube wall decreases monotonically with increasing distance from the tube inlet. Comparison of some computed results with corresponding experimental data is also given.
文摘为了更好地研究直流电弧等离子体炬内的流动与传热,根据磁流体动力学(MHD)理论建立了等离子体电弧区的数学物理模型,采用磁矢量势A的方法来计算磁感应强度B的大小,利用通用软件FLUENT并进行二次开发,采用用户自定义函数(user defined function,UDF)加入磁流体动力学方程组中的源项和物性参数,并利用用户自定义标量方程(user defined scalar,UDS)的方法加入Maxwell方程组,采用SIMPLE算法对电弧区域进行了数值模拟。计算结果表明:等离子体炬内的弧电压随着气体质量流量的增加而增加;等离子体炬内的温度随着气体质量流量的增加而减小,而速度随着气体质量流量的增加而增加;出口处的温度和速度随径向距离的增加而减小,但温度减小的速率增加。这一结果可为实验提供理论指导和参考。
