Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision mod...Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton’s third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx<sub>1</sub>, and slow-jet, vx<sub>2</sub>. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering.展开更多
The problem of evaluating the sensitivity of non-trivial boundary conditions to the onset of azimuthal combustion instability is a longstanding challenge in the development process of mod-ern gas turbines.The difficul...The problem of evaluating the sensitivity of non-trivial boundary conditions to the onset of azimuthal combustion instability is a longstanding challenge in the development process of mod-ern gas turbines.The difficulty lies in how to describe three-dimensional in-and outlet boundary conditions in an artificial computational domain.To date,the existing analytical models have still failed to quantitatively explain why the features of the azimuthal combustion instability of a com-bustor in laboratory environment are quite different from that in a real gas turbine,making the sta-bility control devices developed in laboratory generally lose the effectiveness in practical applications.To overcome this limitation,we provide a novel theoretical framework to directly include the effect of non-trivial boundary conditions on the azimuthal combustion instability.A key step is to take the non-trivial boundary conditions as equivalent distributed sources so as to uniformly describe the physical characteristics of the inner surface in an annular enclosure along with different in-and outlet configurations.Meanwhile,a dispersion relation equation is established by the application of three-dimensional Green's function approach and generalized impedance con-cept.Results show that the effects of the generalized modal reflection coefficients on azimuthal unstable modes are extremely prominent,and even prompt the transition from stable to unstable mode,thus reasonably explaining why the thermoacoustic instability phenomena in a real gas tur-bine are difficult to observe in an isolated combustion chamber.Overall,this work provides an effective tool for analysis of the azimuthal combustion instability including various complicated boundary conditions.展开更多
This paper presents an experimental study on the emission characteristics and combustion instabilities of oxy-fuel combustions in a swirl-stabilized combustor. Different oxygen concentrations (Xoxy=25%～45%, where Xox...This paper presents an experimental study on the emission characteristics and combustion instabilities of oxy-fuel combustions in a swirl-stabilized combustor. Different oxygen concentrations (Xoxy=25%～45%, where Xoxy is oxygen concentra- tion by volume), equivalence ratios (φ=0.75～1.15) and combustion powers (CP=1.08～2.02 kW) were investigated in the oxy-fuel (CH4/CO2/O2) combustions, and reference cases (Xoxy=25%～35%, CH4/N2/O2 flames) were covered. The results show that the oxygen concentration in the oxidant stream significantly affects the combustion delay in the oxy-fuel flames, and the equivalence ratio has a slight effect, whereas the combustion power shows no impact. The temperature levels of the oxy-fuel flames inside the combustion chamber are much higher (up to 38.7%) than those of the reference cases. Carbon monoxide was vastly produced when Xoxy>35% or φ>0.95 in the oxy-fuel flames, while no nitric oxide was found in the exhaust gases because no N2 participates in the combustion process. The combustion instability of the oxy-fuel combustion is very different from those of the reference cases with similar oxygen content. Oxy-fuel combustions excite strong oscillations in all cases studied Xoxy=25%～45%. However, no pressure fluctuations were detected in the reference cases when Xoxy>28.6% accomplished by heavily sooting flames which were not found in the oxy-fuel combustions. Spectrum analysis shows that the frequency of dynamic pressure oscillations exhibits randomness in the range of 50～250 Hz, therefore resulting in a very small resultant amplitude. Temporal oscillations are very strong with amplitudes larger than 200 Pa, even short time fast Fourier transform (FFT) analysis (0.08 s) shows that the pressure amplitude can be larger than 40 Pa.展开更多
The instable combustion or oscillation combustion which occurs in three high capacity solid rocket motors using high energy composite propellant with finocyl grain is studied. The reasons of the acoustic combustion in...The instable combustion or oscillation combustion which occurs in three high capacity solid rocket motors using high energy composite propellant with finocyl grain is studied. The reasons of the acoustic combustion instability are also discussed. Three engineering methods that can eliminate combustion instability are proposed and discussed. The study shows that the combustion instability mainly depends on the propellant grain shape and nozzle structure. Some measures to reduce the acoustic energy and mass generation rate of combustion gas can be adopted. The test results indicate that the modified rocket motors can significantly eliminate the instable combustion and improve the motor internal ballistic performance.展开更多
Moderate or intense lowoxygen dilution(MILD)combustion has become a promising lowNOX emission technology,while the delayed mixing of reactants and slower oxidation rate could potentially cause ignition instability in ...Moderate or intense lowoxygen dilution(MILD)combustion has become a promising lowNOX emission technology,while the delayed mixing of reactants and slower oxidation rate could potentially cause ignition instability in some scenarios.This paper proposes a new idea for enhancing the ignition stability for methane MILD combustion by combining with offstoichiometric combustion(OSC),and its performances have been numerically assessed through a comparison against the original MILD combustion burner.The results reveal although nonpremixed pattern has the lowest NO emission,it suffers from a larger liftoff distance,thus less ignition stability.Contrarily,both partiallypremixed and fully premixed patterns exhibit excellent ignition stability.Among the considered OSC conditions,the pattern of Inner ultrarich and Outer lean produces the lowest NO emission while maintains a high ignition stability.Furthermore,the enhancement of the combustion stability by implementing OSC to the original MILD combustion burner is shown by comparing the operational range of furnace wall temperature(Tf),CO and NO emissions,as well as the evolution of chemical flame.The comparison reveals that OSC can extend the lowest operational Tf from 900 K to 800 K.More importantly,OSC can significantly improve the ignition stability in the whole range of Tf as compared to the original MILD combustion burner.展开更多
The purpose of this study is to investigate means of controlling the interior ballistic stability of a bulk-loaded propellant gun（BLPG）.Experiments on the interaction of twin combustion gas jets and liquid medium in...The purpose of this study is to investigate means of controlling the interior ballistic stability of a bulk-loaded propellant gun（BLPG）.Experiments on the interaction of twin combustion gas jets and liquid medium in a cylindrical stepped-wall combustion chamber are conducted in detail to obtain time series processes of jet expansion,and a numerical simulation under the same working conditions is also conducted to verify the reliability of the numerical method by comparing numerical results and experimental results.From this,numerical simulations on mutual interference and expansion characteristics of multiple combustion gas jets（four,six,and eight jets） in liquid medium are carried out,and the distribution characteristic of pressure,velocity,temperature,and evolutionary processes of Taylor cavities and streamlines of jet flow Held are obtained in detail.The results of numerical simulations show that when different numbers of combustion gas jets expand in liquid medium,there are two different types of vortices in the jet flow field,including corner vortices of liquid phase near the step and backflow vortices of gas phase within Taylor cavities.Because of these two types of vortices,the radial expansion characteristic of the jets is increased,while changing numbers of combustion gas jets can restrain Kelvin-Helmholtz instability to a certain degree in jet expansion processes,which can at last realize the goal of controlling the interior ballistic stability of a BLPG.The optimum method for both suppressing Kelvin-Helmholtz instability and promoting radial expansion of Taylor cavities can be determined by analyzing the change of characteristic parameters in a jet flow field.展开更多
文摘Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton’s third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx<sub>1</sub>, and slow-jet, vx<sub>2</sub>. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering.
基金supported by the Science Center for Gas Turbine Project of China (No.P2022-B-II-013-001)the National Natural Science Foundation of China (No.52106038).
文摘The problem of evaluating the sensitivity of non-trivial boundary conditions to the onset of azimuthal combustion instability is a longstanding challenge in the development process of mod-ern gas turbines.The difficulty lies in how to describe three-dimensional in-and outlet boundary conditions in an artificial computational domain.To date,the existing analytical models have still failed to quantitatively explain why the features of the azimuthal combustion instability of a com-bustor in laboratory environment are quite different from that in a real gas turbine,making the sta-bility control devices developed in laboratory generally lose the effectiveness in practical applications.To overcome this limitation,we provide a novel theoretical framework to directly include the effect of non-trivial boundary conditions on the azimuthal combustion instability.A key step is to take the non-trivial boundary conditions as equivalent distributed sources so as to uniformly describe the physical characteristics of the inner surface in an annular enclosure along with different in-and outlet configurations.Meanwhile,a dispersion relation equation is established by the application of three-dimensional Green's function approach and generalized impedance con-cept.Results show that the effects of the generalized modal reflection coefficients on azimuthal unstable modes are extremely prominent,and even prompt the transition from stable to unstable mode,thus reasonably explaining why the thermoacoustic instability phenomena in a real gas tur-bine are difficult to observe in an isolated combustion chamber.Overall,this work provides an effective tool for analysis of the azimuthal combustion instability including various complicated boundary conditions.
基金Project supported by the National Natural Science Foundation of China (No. 50576081)Zhejiang Provincial Natural Science Foundation of China (No. R107532)+1 种基金Program for the New Century Excellent Talents in University (No. NCET-07-0761)the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 200747)
文摘This paper presents an experimental study on the emission characteristics and combustion instabilities of oxy-fuel combustions in a swirl-stabilized combustor. Different oxygen concentrations (Xoxy=25%～45%, where Xoxy is oxygen concentra- tion by volume), equivalence ratios (φ=0.75～1.15) and combustion powers (CP=1.08～2.02 kW) were investigated in the oxy-fuel (CH4/CO2/O2) combustions, and reference cases (Xoxy=25%～35%, CH4/N2/O2 flames) were covered. The results show that the oxygen concentration in the oxidant stream significantly affects the combustion delay in the oxy-fuel flames, and the equivalence ratio has a slight effect, whereas the combustion power shows no impact. The temperature levels of the oxy-fuel flames inside the combustion chamber are much higher (up to 38.7%) than those of the reference cases. Carbon monoxide was vastly produced when Xoxy>35% or φ>0.95 in the oxy-fuel flames, while no nitric oxide was found in the exhaust gases because no N2 participates in the combustion process. The combustion instability of the oxy-fuel combustion is very different from those of the reference cases with similar oxygen content. Oxy-fuel combustions excite strong oscillations in all cases studied Xoxy=25%～45%. However, no pressure fluctuations were detected in the reference cases when Xoxy>28.6% accomplished by heavily sooting flames which were not found in the oxy-fuel combustions. Spectrum analysis shows that the frequency of dynamic pressure oscillations exhibits randomness in the range of 50～250 Hz, therefore resulting in a very small resultant amplitude. Temporal oscillations are very strong with amplitudes larger than 200 Pa, even short time fast Fourier transform (FFT) analysis (0.08 s) shows that the pressure amplitude can be larger than 40 Pa.
文摘The instable combustion or oscillation combustion which occurs in three high capacity solid rocket motors using high energy composite propellant with finocyl grain is studied. The reasons of the acoustic combustion instability are also discussed. Three engineering methods that can eliminate combustion instability are proposed and discussed. The study shows that the combustion instability mainly depends on the propellant grain shape and nozzle structure. Some measures to reduce the acoustic energy and mass generation rate of combustion gas can be adopted. The test results indicate that the modified rocket motors can significantly eliminate the instable combustion and improve the motor internal ballistic performance.
基金the National Natural Science Foundation of China(52006077)Innovation Research Foundation of Huazhong University of Science and Technology(5001120031).
文摘Moderate or intense lowoxygen dilution(MILD)combustion has become a promising lowNOX emission technology,while the delayed mixing of reactants and slower oxidation rate could potentially cause ignition instability in some scenarios.This paper proposes a new idea for enhancing the ignition stability for methane MILD combustion by combining with offstoichiometric combustion(OSC),and its performances have been numerically assessed through a comparison against the original MILD combustion burner.The results reveal although nonpremixed pattern has the lowest NO emission,it suffers from a larger liftoff distance,thus less ignition stability.Contrarily,both partiallypremixed and fully premixed patterns exhibit excellent ignition stability.Among the considered OSC conditions,the pattern of Inner ultrarich and Outer lean produces the lowest NO emission while maintains a high ignition stability.Furthermore,the enhancement of the combustion stability by implementing OSC to the original MILD combustion burner is shown by comparing the operational range of furnace wall temperature(Tf),CO and NO emissions,as well as the evolution of chemical flame.The comparison reveals that OSC can extend the lowest operational Tf from 900 K to 800 K.More importantly,OSC can significantly improve the ignition stability in the whole range of Tf as compared to the original MILD combustion burner.
基金supported by National Natural Science Foundation of China(Grant 11372139)
文摘The purpose of this study is to investigate means of controlling the interior ballistic stability of a bulk-loaded propellant gun（BLPG）.Experiments on the interaction of twin combustion gas jets and liquid medium in a cylindrical stepped-wall combustion chamber are conducted in detail to obtain time series processes of jet expansion,and a numerical simulation under the same working conditions is also conducted to verify the reliability of the numerical method by comparing numerical results and experimental results.From this,numerical simulations on mutual interference and expansion characteristics of multiple combustion gas jets（four,six,and eight jets） in liquid medium are carried out,and the distribution characteristic of pressure,velocity,temperature,and evolutionary processes of Taylor cavities and streamlines of jet flow Held are obtained in detail.The results of numerical simulations show that when different numbers of combustion gas jets expand in liquid medium,there are two different types of vortices in the jet flow field,including corner vortices of liquid phase near the step and backflow vortices of gas phase within Taylor cavities.Because of these two types of vortices,the radial expansion characteristic of the jets is increased,while changing numbers of combustion gas jets can restrain Kelvin-Helmholtz instability to a certain degree in jet expansion processes,which can at last realize the goal of controlling the interior ballistic stability of a BLPG.The optimum method for both suppressing Kelvin-Helmholtz instability and promoting radial expansion of Taylor cavities can be determined by analyzing the change of characteristic parameters in a jet flow field.
