Academic literature on the topic 'Ideal rocket equation'
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Journal articles on the topic "Ideal rocket equation"
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Li, Xuge. "Comprehensive Exploration on Performance Improvement of Rocket Thruster." Highlights in Science, Engineering and Technology 88 (March 29, 2024): 847–52. http://dx.doi.org/10.54097/bnr30f66.
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Since mankind has been carrying out space research for decades, rockets are one of the most important tools used by mankind to explore space. In this article, the structure of a rocket is analyzed, and the function of each part is understood. Tsolkovsky's rocket equation is used to analyze the relationship between the initial and final mass of the rocket. Through the study of engine thrust, the calculation of engine thrust was demonstrated using the formula. Besides, the ideal specific impulse of different fuels in a vacuum is compared in a graph and some of the fuels in the chart. Ultimately, it was concluded that the performance of rockets could be improved in terms of open-edge construction, enhanced engine thrust, utilization of composite fuels and improved combustion efficiency. In the future, due to the development of rocket technology, perhaps commercial space activities will usher in a new trend.
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D’Alessandro, Simone, Marco Pizzarelli, and Francesco Nasuti. "A Hybrid Real/Ideal Gas Mixture Computational Framework to Capture Wave Propagation in Liquid Rocket Combustion Chamber Conditions." Aerospace 8, no. 9 (2021): 250. http://dx.doi.org/10.3390/aerospace8090250.
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The present work focuses on the development of new mathematical and numerical tools to deal with wave propagation problems in a realistic liquid rocket chamber environment. A simplified real fluid equation of state is here derived, starting from the literature. An approximate Riemann solver is then specifically derived for the selected conservation laws and primitive variables. Both the new equation of state and the new Riemann solver are embedded into an in-house one-dimensional CFD solver. The verification and validation of the new code against wave propagation problems are then performed, showing good behavior. Although such problems might be of interest for different applications, the present study is specifically oriented to the low order modeling of high-frequency combustion instability in liquid-propellant rocket engines.
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Yang, Yuqi, Longbin Liu, and Moyan Chen. "Study on thrust performance of small water rocket launch." Journal of Physics: Conference Series 2313, no. 1 (2022): 012021. http://dx.doi.org/10.1088/1742-6596/2313/1/012021.
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Abstract For water rocket test of low cost, quick assembly and simple, based on the single water rocket, using Bernoulli equation, the ideal gas adiabatic model and mass conservation theorem, this paper derived both the calculation method of thrust rocket the bottle under the different initial water volume ratio of water pressure, and the rule about how the water rocket thrust and pressure performance change. It is found that the pressure, the jet velocity of the water relative to the water rocket body and thrust of water rocket will decrease with the decrease of water amount under different initial charging pressure and different initial water amount. If the initial pressure is higher, the water rocket will gain more energy and launch faster; However, it doesn’t mean that the more initial water storage ratio is, the better. The maximum velocity obtained by water rocket under the same initial pressure increases first and then decreases with the initial water storage ratio and the optimal initial water storage ratio increases with the increase of initial pressure. According to data calculation, the numerical value increases with the increase of initial pressure. The optimal performance of water rocket can be obtained by taking the maximum pressure and the corresponding optimal initial injection water when the water rocket body is allowed.
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Hu, Haifeng, Xinni Gao, Yushan Gao, and Jianwen Yang. "Shock Wave and Aeroelastic Coupling in Overexpanded Nozzle." Aerospace 11, no. 10 (2024): 818. http://dx.doi.org/10.3390/aerospace11100818.
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The growing demand for increasing the engine power of a liquid rocket is driving the development of high-power De-Laval nozzles, which is primarily achieved by increasing the expansion ratio. A high-expansion-ratio for De-Laval nozzles can cause flow separation, resulting in unsteady, asymmetric forces that can limit nozzle life. To enhance nozzle performance, various separation control methods have been proposed, but no methods have been fully implemented thus far due to the uncertainties associated with simulating flow phenomena. A numerical study of a high-area-ratio rocket engine is performed to analyze the aeroelastic performance of its structure under flow separation conditions. Based on numerical methodology, the flow inside a rocket nozzle (the VOLVO S1) is analyzed, and different separation patterns are comprehensively discussed, including both free shock separation (FSS) and restricted shock separation (RSS). Since the location of the flow separation point strongly depends on the turbulence model, both the single transport equation and two-transport-equation turbulence models are simulated, and the findings are compared with the experimental results. Therefore, the Spalart–Allmaras (SA) turbulence model is the ideal choice for this rocket nozzle geometry. A wavelet is used to analyze the amplitude frequencies from 0 to 100 Hz under various pressure fluctuation conditions. Based on a clear understanding of the flow field, an aeroelastic coupling method is carried out with loosely coupled computational fluid dynamics (CFD)/computational structural dynamics (CSD). Some insights into the aeroelasticity of the nozzle under separated flow conditions are obtained. The simulation results show the significant impact of the structural response on the inherent pressure pulsation characteristics resulting from flow separation.
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Akiki, M., and J. Majdalani. "Compressible integral representation of rotational and axisymmetric rocket flow." Journal of Fluid Mechanics 809 (November 9, 2016): 213–39. http://dx.doi.org/10.1017/jfm.2016.654.
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This work focuses on the development of a semi-analytical model that is appropriate for the rotational, steady, inviscid, and compressible motion of an ideal gas, which is accelerated uniformly along the length of a right-cylindrical rocket chamber. By overcoming some of the difficulties encountered in previous work on the subject, the present analysis leads to an improved mathematical formulation, which enables us to retrieve an exact solution for the pressure field. Considering a slender porous chamber of circular cross-section, the method that we follow reduces the problem’s mass, momentum, energy, ideal gas, and isentropic relations to a single integral equation that is amenable to a direct numerical evaluation. Then, using an Abel transformation, exact closed-form representations of the pressure distribution are obtained for particular values of the specific heat ratio. Throughout this effort, Saint-Robert’s power law is used to link the pressure to the mass injection rate at the wall. This allows us to compare the results associated with the axisymmetric chamber configuration to two closed-form analytical solutions developed under either one- or two-dimensional, isentropic flow conditions. The comparison is carried out assuming, first, a uniformly distributed mass flux and, second, a constant radial injection speed along the simulated propellant grain. Our amended formulation is consequently shown to agree with a one-dimensional solution obtained for the case of uniform wall mass flux, as well as numerical simulations and asymptotic approximations for a constant wall injection speed. The numerical simulations include three particular models: a strictly inviscid solver, which closely agrees with the present formulation, and both $k$–$\unicode[STIX]{x1D714}$ and Spalart–Allmaras computations.
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Knoetze, J. H. "Die berekening van die stukrag van ’n vuurpylmotor." Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 12, no. 3 (1993): 67–71. http://dx.doi.org/10.4102/satnt.v12i3.565.
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Traditionally the thrust of a rocket motor is calculated by first calculating the thrust coefficient and then multiplying it by the product of the throat area and pressure. The thrust coefficient is calculated using a standard gas dynamics equation. This equation assumes that the combustion products are a single component, non-reacting ideal gas and that the flow through the nozzle is isentropic. The thrust coefficient is a function of the ratio of specific heats, y, the area ratio of the nozzle and the motor and ambient pressures. Standard methods exist for calculating the tosses due to deviations from the assumed flow. The combustion products of modern composite propellants contain a significant portion of condensed species (primarily A1₂O₃), while the composition of the combustion products changes continuously as the products move throught the nozzle. Some uncertainty therefore exists with regard to which value of y to use and how to handle the condensed species. The assumption o f an ideat, non-reacting gas can be el iminated hy as.mming the process to he isentropic and to calculate the thrust hy using the thermodynamic state and composition of the combustion products in the motor and nozzle exit. This can be achieved by using any of the standard thermochemistry programs available in the rocket industry. It is thus possible to use the results of a standard thermochemistry program directly in an alternative method for calculating thrust. Using this method only the mass flow rate (which is a function of pressure, throat area and effective caracteristic velocity) and the results from the thermochemistry program are needed to calculate the thrust. The advantages of the alternative method are illustrated by comparing the results of the two methods with a measured thrust curve.
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Costa, Fernando S., and Gustavo A. A. Fischer. "Propulsion and Thermodynamic Parameters of van der Waals Gases in Rocket Nozzles." International Journal of Aerospace Engineering 2019 (August 14, 2019): 1–11. http://dx.doi.org/10.1155/2019/3139204.
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Propellants or combustion products can reach high pressures and temperatures in advanced or conventional propulsion systems. Variations in flow properties and the effects of real gases along a nozzle can become significant and influence the calculation of propulsion and thermodynamic parameters used in performance analysis and design of rockets. This work derives new analytical solutions for propulsion parameters, considering gases obeying the van der Waals equation of state with specific heats varying with pressure and temperature. Steady isentropic one-dimensional flows through a nozzle are assumed for the determination of specific impulse, characteristic velocity, thrust coefficient, critical flow constant, and exit and throat flow properties of He, H2, N2, H2O, and CO2 gases. Errors of ideal gas solutions for calorically perfect and thermally perfect gases are determined with respect to van der Waals gases, for chamber temperatures varying from 1000 to 4000 K and chamber pressures from 5 to 35 MPa. The effects of covolumes and intermolecular attraction forces on flow and propulsion parameters are analyzed.
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TAKAHASHI, Ryuji, Nobuyuki TSUBOI, Takashi TOKUMASU, and Shin-ichi TSUDA. "Validation of Soave–Redlich–Kwong equation of state coupled with a classical mixing rule for sound speed of non-ideal gas mixture of oxygen-hydrogen as liquid rocket propellants." Journal of Thermal Science and Technology 18, no. 1 (2023): 22–00365. http://dx.doi.org/10.1299/jtst.22-00365.
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Дубровський, І. Д., and В. Л. Бучарський. "THE APPLICATION OF THE EXTENDED CELLS METHOD TO SIMULATE THE FLOW OF COMBUSTION GASES IN THE LPRE CHAMBER." Journal of Rocket-Space Technology 31, no. 4 (2023): 32–39. http://dx.doi.org/10.15421/452305.
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 Abstract. The numerical modeling of the process of two-dimensional axisymmetric flow of combustion gases in the chamber of a liquid rocket engine is considered in this study. In general, when solving such problems, meshes are used which lines coincide with the boundaries of the computational domain. However, an alternative solution is proposed here, which is to apply the extended cells method. It allows using rectangular Cartesian grids, which lines do not coincide with the boundaries of the computational domain, without reducing the stability of the numerical solution due to the fractional finite volumes. This also simplifies the setting of boundary conditions in such volumes. The advantage of the proposed approach over the generally accepted one is the absence of the global geometric transformations during the entire modelling process, which leads to a reduction in its duration. To perform the numerical modelling, an inviscid ideal compressible gas of constant chemical composition was chosen as a basic model of a continuum. It is described by a system of the unsteady Euler equations in integral form, which was closed by the Mendeleev-Clapeyron equation of state. For the numerical solution of this system, the finite volume method was used with the reconstruction of the flow parameters by the WENO algorithm of the third order of accuracy. The solution of the Riemann problem was carried out using the Lax-Friedrichs relations. Time integration of the system of equations was performed using the explicit Runge-Kutta method of the third order of accuracy. All calculations were carried out on a uniform rectangular Cartesian mesh, which lines did not coincide with the boundaries of the computational domain. The results were compared with the solution of the same problem using the ANSYS Fluent on an unstructured mesh coinciding with the boundaries of the computational domain. The value of the relative error obtained as a result of comparing both solutions did not exceed 0.05.
 
 
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Fu, Jia, and Chaoqi Xia. "Microstructure Evolution and Mechanical Properties of X6CrNiMoVNb11-2 Stainless Steel after Heat Treatment." Materials 14, no. 18 (2021): 5243. http://dx.doi.org/10.3390/ma14185243.
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X6CrNiMoVNb11-2 supermartensitic stainless steel, a special type of stainless steel, is commonly used in the production of gas turbine discs in liquid rocket engines and compressor disks in aero engines. By optimizing the parameters of the heat-treatment process, its mechanical properties are specially adjusted to meet the performance requirement in that particular practical application during the advanced composite casting-rolling forming process. The relationship between the microstructure and mechanical properties after quenching from 1040 °C and tempering at 300–670 °C was studied, where the yield strength, tensile strength, elongation and impact toughness under different cooling conditions are obtained by means of mechanical property tests. A certain amount of high-density nanophase precipitation is found in the martensite phase transformation through the heat treatment involved in the quenching and tempering processes, where M23C6 carbides are dispersed in lamellar martensite, with the close-packed Ni3Mo and Ni3Nb phases of high-density co-lattice nanocrystalline precipitation created during the tempering process. The ideal process parameters are to quench at 1040 °C in an oil-cooling medium and to temper at 650 °C by air-cooling; final hardness is averaged about 313 HV, with an elongation of 17.9%, the cross-area reduction ratio is 52%, and the impact toughness is about 65 J, respectively. Moreover, the tempered hardness equation, considering various tempering temperatures, is precisely fitted. This investigation helps us to better understand the strengthening mechanism and performance controlling scheme of martensite stainless steel during the cast-rolling forming process in future applications.
Book chapters on the topic "Ideal rocket equation"
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Takabe, Hideaki. "Shock Waves and Ablation Dynamics." In Springer Series in Plasma Science and Technology. Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-45473-8_3.
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AbstractWhen an intense laser is irradiated on a solid target, the laser energy is absorbed on the surface so that the material becomes plasma to expand into the vacuum region. Through the laser-plasma interaction, the laser energy heats the expanding region spreading by its sound velocity. As the result the expanding region has the temperature ~ 1 keV and the pressure reaches 100 Mbar (10TPa). Since the laser is absorbed near relatively high density (~cut-off density), the plasma can be assumed to be in LTE and hydrodynamic description is acceptable.The surface pressure called ablation pressure drives strong shock waves in the solid material as if the solid is almost gas. The shock wave physics is briefly reviewed to use the Rankin-Hugoniot (RH) relation, although detail studied is needed for the equation of state of the compressed matter. By use of the ablation pressure, it is possible to accelerate a thin material to higher velocity like a rocket propulsion.One dimensional hydrodynamics is reviewed for steady state and time dependent dynamics within the ideal fluid assumption. Deflagration and detonation waves are also explained as jump condition with energy deposition. The laser implosion dynamics is compered between stationary solutions, computational results, and the experimental data. The importance of validation of simulation codes is discussed.
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Dias Filho José Luiz Ernandes, Santos Vitor Guimarães Pereira, Maia Paulo Cesar Almeida, and Xavier Gustavo de Castro. "Study of Relationship Between Wear Tests on Rocks by Slake Durability, Micro-Deval and Los Angeles Abrasion Tests." In Integrating Innovations of Rock Mechanics. IOS Press, 2015. https://doi.org/10.3233/978-1-61499-605-7-225.
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This paper presents a critical analysis of three major wear tests on rock: slake durability, Los Angeles and micro-Deval. These tests are amply used as a way to characterize the rocks used in construction. With large scale projects of infrastructure across the country and around the world at an accelerated rate, the growing search for more rock materials, it generates an increasing demand of characterization for wear test. With the different exogenous environment in which there are geotechnical applications, the rock can suffer from various forms of degradation in the service time. Wear tests generate good results of durability and weight loss, which are the main factor of choice of rocks in the construction. The objective of this paper is to propose a correlation between these tests as [1] concludes his paper with the linear relationship of slake durability and micro-Deval test and proposing an idea of direct correlation to further testing and characterization deeper. The main variations of the tests are discussed in the literature and presented the results of the main adjustments made in abrasive tests and their characteristics. Analysis of the results shows and confirms the previous idea and presents equations of correlation between the wear tests presented. The idea is not to discard the use of characterization tests, but rather to broaden the discussion on the subject and provide an alternative to laboratories with the absence of one or other equipment.
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Mazur, Joseph. "Curious Beginnings." In Enlightening Symbols. Princeton University Press, 2016. http://dx.doi.org/10.23943/princeton/9780691173375.003.0001.
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This chapter traces the beginnings of mathematical notation. For tens of thousands of years, humans had been leaving signification marks in their surroundings, gouges on trees, footprints in hard mud, scratches in skin, and even pigments on rocks. A simple mark can represent a thought, indicate a plan, or record a historical event. Yet the most significant thing about human language and writing is that speakers and writers can produce a virtually infinite set of sounds, declarations, notions, and ideas from a finite set of marks and characters. The chapter discusses the emergence of the alphabet, counting, and mathematical writing. It also considers the discovery of traces of Sumerian number writing on clay tablets in caves from Europe to Asia, the use of Egyptian hieroglyphics, and algebra problems in the Rhind (or Ahmes) papyrus that presented simple equations without any symbols other than those used to indicate numbers.
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Oreskes, Naomi. "Drift Mechanisms in the 1920s." In The Rejection of Continental Drift. Oxford University Press, 1999. http://dx.doi.org/10.1093/oso/9780195117325.003.0010.
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The final chapter of the third edition of The Origin of Continents and Oceans was devoted to the dynamic causes of drift, and Wegener’s tone in these final fifteen pages was decidedly more tentative than in the rest. Frankly acknowledging the huge uncertainties surrounding this issue, he proceeded on the basis of a phenomenological argument. Mountains, Wegener pointed out, are not randomly distributed: they are concentrated on the western and equatorial margins of continents. The Andes and Rockies, for example, trace the western margins of North and South America; the Alps and the Himalayas follow a latitudinal trend on their equatorial sides of Europe and Asia. If mountains are the result of compression on the leading edges of drifting continents, then the overall direction of continental drift must be westward and equatorial. Continental displacements are not random, as the English word drift might imply, but coherent. This coherence had been the inspiration for an earlier version of drift proposed by the American geologist Frank Bursley Taylor (1860–1938). A geologist in the Glacial Division of the U.S. Geological Survey under T. C. Chamberlin, Taylor was primaril known for his work on the Pleistocene geology of the Great Lakes region. But his knowledge extended beyond regional studies: as a special student at Harvard, he had studied geology and astronomy; as a survey geologist under the influence of Chamberlin and G. K. Gilbert, he had published a number of articles on theoretical problems. One of these was an 1898 pamphlet outlining a theory of the origin of the moon by planetary capture; in 1903, Taylor developed his theoretical ideas more fully in a privately published book. Turning the Darwin–Fisher fissiparturition hypothesis on its head, Taylor proposed that the moon had not come from the earth but had been captured by it after the close approach of a cornet. Once caught, (lie tidal effect of the moon increased the speed of the earth’s rotation and pulled the continents away from the poles toward the equator. In 1910, Taylor pursued the geological implications of this idea in an article in the Bulletin of the Geological Society of America entitled “Bearing of the Tertiary Mountain Belt on the Origin of the Earth’s Plan.”
Conference papers on the topic "Ideal rocket equation"
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Akyuzlu, K. M., K. Albayrak, and C. Karaeren. "A Numerical Study of Thermoacoustic Oscillations in a Rectangular Channel Using CMSIP Method." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-13109.
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This paper presents a mathematical model that was developed to study instabilities (primarily thermoacoustic oscillations) experienced inside a channel (with a rectangular cross section) heated symmetrically (from its top and bottom.) The heated channel is configured to simulate a combustion chamber of a rocket hybrid rocket motor and is connected to a converging–diverging nozzle in the downstream and to a plenum with a flow straightener in the upstream side. The working fluid is supplied from a pressurized storage tank to the upstream plenum through a throttle valve. A multi-component approach is used to model this test apparatus. In this integrated component model, the unsteady flow through the throttle valve and the nozzle is assumed to be one-dimensional and isentropic where as the flow in the forward plenum and the heated channel is assumed to be a two-dimensional, unsteady, compressible, turbulent, and subsonic. The physics based mathematical model of the flow in the channel consists of conservation of mass, momentum (two-dimensional Navier-Stokes) and energy equations subject to appropriate boundary conditions as defined by the physical problem stated above. The working fluid is assumed to be compressible where the density of the fluid is related to the pressure and temperature of the fluid through a simple ideal gas relation. The governing equations are discretized using second order accurate central differencing for spatial derivatives and second order accurate (based on Taylor expansion) finite difference approximations for temporal derivatives. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns (primitive variables, i.e., pressure, temperature, and the velocity field) of the problem. The turbulence model equations and the unsteady flow equation for the throttle valve are solved using a second order accurate explicit finite difference technique. Convergence and grid independence studies were done to determine the optimum mesh size and computational time increment. Furthermore, two benchmark cases (unsteady driven cavity and laminar channel flows) were simulated using the developed numerical model to verify the accuracy of the proposed solution procedure. Numerical experiments were then carried out to simulate the thermoacoustic oscillations inside rectangular channels with various aspect ratios ranging from 5 to 20 for various operating conditions (i.e., for Re numbers between 102 and 106) and to determine the flow regions where these oscillations are sustained. The numerical simulation results indicate that the mathematical model for the gas flow in the heated channel predicts the expected unsteady temperature and pressure distributions, and the velocity field, successfully. Furthermore, it is concluded that the proposed integrated component model is successful in generating the characteristics of the instabilities associated with thermal, hydrodynamic, and thermoacoustic oscillations in heated channels.
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Miao, Yunfei, Guoping Wang, Xiaoting Rui, Tianxiong Tu, and Lilin Gu. "Test Dynamics Method of Non-Full Loading Firing for Multiple Launch Rocket System Using Transfer Matrix Method for Multibody Systems." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85784.
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This paper studies test dynamics method of non-full loading firing for multiple launch rocket system (MLRS) and provides a new test method for reducing rocket consumption in MLRS firing precision test. Based on the theories of launch dynamics and Rui method, namely the transfer matrix method for multibody systems (MSTMM), launch dynamics model, characteristic equations and dynamics response equations of MLRS are established. The launch and flight dynamic simulation system for MLRS is developed combining the Monte Carlo simulation technology. The simulated results of vibration characteristics, rocket initial disturbance, and firing precision are verified by modal test, pulse thrust test and firing test, which show the simulation system can more accurately reflect the dynamic characteristics of the actual system and its dynamics computation has sufficient accuracy. The relationship between the initial state of MLRS and the mean value and median error of the impact points are established. Based on the idea of equal initial disturbance, non-full loading firing test dynamics method is presented for reducing the rocket consumption in firing precision test, by optimizing the loading position, firing orders and firing intervals of the rockets. For a practical MLRS, a seven-shot test scheme is designed and tested. The experimental results show that the amount of the rockets in firing precision test is reduce by 61% compared with the conventional test method, which saves a lot of testing costs.
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Danov, Stanislav N., and Ashwani K. Gupta. "Influence of Imperfections in Working Media on Diesel Engine Indicator Process: Part 1 — Theory." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/cie-6026.
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Abstract Several improvements to the mathematical model of the indicator process, taking place in a diesel engine cylinder, are proposed. The thermodynamic behavior of working media is described by the equation of state, valid for real gases. Analytical mathematical dependencies between thermal parameters (pressure, temperature, volume) and caloric parameters (internal energy, enthalpy, specific heat capacities) have been obtained. These equations have been applied to the various products encountered during the burning of fuel and the gas mixture as a whole in the engine cylinder under conditions of high pressures and temperatures. An improved mathematical model, based on the first law of thermodynamics, has been developed by taking into account imperfections in the working media that appear under high pressures and temperatures. The numerical results show that there are significant differences between the values calculated using ideal gas behavior and the real gas, in particular at high pressure and high temperature conditions. The numerical experiments show that if the pressure is above 8 to 9 MPa, the imperfections in working medium must be taken into consideration. The results obtained from the mathematical dependency of the caloric parameters can also be used to model any energy conversion and combustion process, such as, advanced gas turbine engines which operate at high pressure ratios, rockets.
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Abdullah, Eassa, Mobarak Baatiyah, Jaber Aljabri, et al. "Developing a Generalized Correlation to Obtain Steady-State Based Permeability Using a Probe Permeameter." In SPE Reservoir Characterisation and Simulation Conference and Exhibition. SPE, 2023. http://dx.doi.org/10.2118/212639-ms.
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Abstract The importance of permeability cannot be under-stimated. It is used in crucial equations used to determine quantities analysed by reservoir, drilling, and production engineers. Using permeability along with other properties is important to understanding reservoir behaviour when wells are drilled, to calculate the rate of the fluid flow, as illustrated by Darcy's equation that relates fluid flow to permeability. Measuring permeability in the laboratory with the conventioanl available steady-state equipment can be time consuming, especially if it was done by gas injection which requires measuring at different pressure points to satisfy Klinkenberg equation. A quick measuring equipment called the prob permeameter have been used for many years, it quantitatively performs a permeability point measurement as a function of position on either a whole core, slabbed core or a rock slab. However, despite of its prompt and easy measurement, most of the results represents a general idea about the actual permeability and sometimes even falls out of the range, which makes it unrelaiable. Series of experiments were conducted for a variety of rock samples with a wide range of permeability ranging from tight to permeable, to compare the generated results between both of the above equipment. The results were graphed and been compared using different point of views, mathematicalwise, petroleum engineeringwise, and geologicalwise. Ultimately, an equation to correlate between the results was developed graphically and using logistic regression techniques.
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Akyuzlu, K. M., and K. Albayrak. "A Numerical Study of Coupling of Thermal and Hydrodynamic Oscillations in a Hybrid Rocket Motor." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-64327.
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A one-dimensional, mathematical model is adopted to investigate, numerically, the instabilities experienced inside a hybrid rocket propulsion system. The presumption is that such oscillations feed into combustion instabilities and result in poor performance of the propulsion system and/or result in mechanical vibrations that lead to failure of the rocket motor. The model adopted for the numerical study is a one-dimensional, multi-node representation of a subscale hybrid rocket propulsion system. A one dimensional channel with circular cross-section is configured to simulate a combustion chamber of a rocket hybrid rocket motor and is connected to a converging–diverging nozzle in the downstream and to a plenum with a flow straightener in the upstream side. The working fluid is supplied from a pressurized storage tank to the upstream plenum through a throttle valve. A multi-component approach is used to model, mathematically, the propulsion system. In this integrated-component model, the unsteady flow through the throttle valve and the nozzle is assumed to be one-dimensional and isentropic whereas the flow in the forward plenum and in the combustion chamber is assumed to be a one-dimensional, unsteady, compressible, turbulent, and subsonic. The physics based mathematical model of the flow in the channel consists of conservation of mass, momentum and energy equations subject to appropriate boundary conditions as defined by the physical problem stated above. The working fluid is assumed to be compressible through a simple ideal gas relation. The governing equations of the compressible flow in the combustion chamber are discretized using the second order accurate MacCormack finite difference scheme. Convergence and grid independence studies were done to determine the optimum mesh size and computational time increment needed for the present simulations. Furthermore, steady state results of the proposed model are compared to the results of the isentropic, Fanno (viscous 1-D flow), and Rayleigh (1-D flow with heat input) case studies to verify the accuracy of the numerical predictions. Numerical experiments were then carried out to simulate the flow oscillations in the combustion chamber of a sample subscale hybrid rocket motor. Experiments were repeated for various operating conditions (Re numbers between 104 and 106) to determine the flow regions where these oscillations are sustained. The numerical simulation results indicate that the proposed mathematical model predicts the expected unsteady axial distributions of temperature, velocity, and pressure in the combustion chamber and the general characteristics of the experimentally observed instabilities associated with hybrid rocket propulsion systems.
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Danov, Stanislav N., and Ashwani K. Gupta. "Influence of Imperfections in the Working Media on Diesel Engine Indicator Process: Part 2 — Results." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/cie-6027.
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Abstract In the companion Part 1 of this two-part series paper several improvements to the mathematical model of the energy conversion processes, taking place in a diesel engine cylinder, have been proposed. Analytical mathematical dependencies between thermal parameters (pressure, temperature, volume) and caloric parameters (internal energy, enthalpy, specific heat capacities) have been obtained. These equations have been used to provide an improved mathematical model of diesel engine indicator process. The model is based on the first law of thermodynamics, by taking into account imperfections in the working media which appear when working under high pressures and temperatures. The numerical solution of the simultaneous differential equations is obtained by Runge-Kutta type method. The results show that there are significant differences between the values calculated by equations for ideal gas and real gas under conditions of high pressures and temperatures. These equations are then used to solve the desired practical problem in two different two-stroke turbo-charged engines (8DKRN 74/160 and Sulzer-RLB66). The numerical experiments show that if the pressure is above 8 to 9 MPa, the working medium imperfections must be taken into consideration. The mathematical model presented here can also be used to model combustion process of other thermal engines, such as advanced gas turbine engines and rockets.
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Akyuzlu, K. M. "A Numerical Study of High Temperature and High Velocity Gaseous Hydrogen Flow in a Cooling Channel of a Nuclear Thermal Rocket Core." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-38438.
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Two mathematical models (a one-dimensional and a two-dimensional) were adopted to study, numerically, the thermal hydrodynamic characteristics of flow inside the cooling channels of a Nuclear Thermal Rocket (NTR) engine. In the present study, only a single one of the cooling channels of the reactor core is simulated. The one-dimensional model adopted here assumes the flow in this cooling channel to be steady, compressible, turbulent, and subsonic. The physics based mathematical model of the flow in the channel consists of conservation of mass, momentum, and energy equations subject to appropriate boundary conditions as defined by the physical problem stated above. The working fluid (gaseous hydrogen) is assumed to be compressible through a simple ideal gas relation. The physical and transport properties of the hydrogen is assumed be temperature dependent. The governing equations of the compressible flow in cooling channels are discretized using the second order accurate MacCormack finite difference scheme. Convergence and grid independence studies were done to determine the optimum computational cell mesh size and computational time increment needed for the present simulations. The steady state results of the proposed model were compared to the predictions by a commercial CFD package (Fluent.) The two-dimensional CFD solution was obtained in two domains: the coolant (gaseous hydrogen) and the ZrC fuel cladding. The wall heat flux which varied along the channel length (as described by the nuclear variation in the nuclear power generation) was given as an input. Numerical experiments were carried out to simulate the thermal and hydrodynamic characteristics of the flow inside a single cooling channel of the reactor for a typical NERVA type NTR engine where the inlet mass flow rate was given as an input. The time dependent heat generation and its distribution due to the nuclear reaction taking place in the fuel matrix surrounding the cooling channel. Numerical simulations of flow and heat transfer through the cooling channels were generated for steady state gaseous hydrogen flow. The temperature, pressure, density, and velocity distributions of the hydrogen gas inside the coolant channel are then predicted by both one-dimensional and two-dimensional model codes. The steady state predictions of both models were compared to the existing results and it is concluded that both models successfully predict the steady state fluid temperature and pressure distributions experienced in the NTR cooling channels. The two dimensional model also predicts, successfully, the temperature distribution inside the nuclear fuel cladding.
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Ma, Zhengchao, Maoya Hsu, Hao Hu, et al. "Hybrid Strategies for Interpretability of Rate of Penetration Prediction: Automated Machine Learning and SHAP Interpretation." In 58th U.S. Rock Mechanics/Geomechanics Symposium. ARMA, 2024. http://dx.doi.org/10.56952/arma-2024-0315.
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ABSTRACT: Accurate prediction of rate of penetration (ROP) during petroleum drilling is crucial to optimize and guide field operations. However, due to the complex nonlinear relationship between drilling parameters and ROP, traditional empirical models often struggle to accurately predict ROP. This study introduces an automated machine learning (AutoML) for ROP prediction and utilizes SHAP (SHapley Additive exPlanations) to interpret the prediction results. The workflow framework based on this collaborative prediction strategy enables automated processing of data and automatic stacking ensemble of multiple machine learning models. It adaptively selects the optimal model after comprehensive validation without human intervention, thereby significantly reducing the time spent on model selection and hyperparameter optimization for ROP prediction. The results indicate that the weighted ensemble model, which has been stacked level-3 and 5-fold cross-validation, achieves the best prediction accuracy: RMSE= 1.86, MSE= 3.47. SHAP provides a global explanation for the model's prediction results, making the results of the automated prediction workflow more convincing and interpretable. This study provides automated machine learning workflow ideas for accurate prediction of ROP so that researchers can focus more on the business scenario itself without excessive machine knowledge and frequent manual intervention. 1. INTRODUCTION In the field of petroleum drilling, the rate of penetration (ROP) is a crucial indicator that reflects the speed at which the drill bit penetrates and breaks through the rock formation. It plays a pivotal role in measuring drilling efficiency. Accurate prediction of ROP is essential for optimizing drilling parameters during the drilling process, which can effectively improve efficiency and reduce costs (Li et al., 2022; H. Zhang et al., 2021; Kuang et al., 2021). With the development of oil drilling technology and modern data science and technology, the prediction methods for ROP have undergone distinct stages of development: empirical or physical models, prediction models that combine physical and data-driven approaches, and machine learning models (Boukredera et al., 2023; Ahmed et al., 2019). In the realm of equation-based prediction using conventional methods, several physics-based models such as the B-Y ROP equation (Bourgoyne & Young, 1974), MSE equation(Caicedo et al., 2005), and Motahhari equation(Motahhari et al., 2010) have certain limitations. These models may not consider all the factors comprehensively, making it challenging to adapt to complex downhole scenarios. Hegde et al.(2017) compared three physics-based traditional models with data-driven models using a combination of physics and data-driven modeling approaches. In terms of using machine learning to predict ROP, various machine learning algorithms such as random forest(RF), support vector machine(SVM), and neural network(NN) have been employed(Moran et al., 2010; Ashrafi et al., 2019; Brenjkar & Biniaz Delijani, 2022; Tunkiel et al., 2022; C. Zhang et al., 2023; Wan et al., 2023). The results indicate that machine learning outperforms traditional models (Soares & Gray, 2019); Bizhani and Kuru(2022) explored the application of Bayesian neural networks in ROP prediction, focusing on the concept of model prediction uncertainty. Duru(2022) optimized five machine learning algorithms: linear regression, decision tree, support vector machine, random forest and multilayer perceptron by genetic algorithm and the results showed enhanced prediction performance of models. Gan et al.(2023) proposed a novel ROP modeling approach called hybrid bat algorithm optimized - restricted Boltzmann machine - back propagation neural network. Qu et al. (2023) improved the backpropagation neural network (BP) and utilized it for ROP prediction methods.
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Lgotina, Ekaterina, Simon Mathias, Marti Lloret-Cabot, and Andrew Ireson. "Mathematical modelling of pressure induced freezing point depression within soils exhibiting strong capillary pressure effect." In UK Association for Computational Mechanics Conference 2024. Durham University, 2024. http://dx.doi.org/10.62512/conf.ukacm2024.079.
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Many geotechnical applications are affected by the melting and formation of ice in soils. Current state of practice involves incorporating the presence of ice within hydrological models for unsaturated soils using the so-called generalised Clapeyron equation [1]. This represents a modification of the conventional Clapeyron equation by allowing for the pressure in ice and liquid to be different at an ice-liquid interface. Such an idea has come about due to the effects of surface tension, which become important within the pores of porous materials such as soil and rock. However, a common assumption when using the generalised Clapeyron equation is that the ice pressure remains constant [2], which leads to unrealistic behaviour in the presence of significant pore-water pressure changes. Here we develop a new mathematical modelling framework to explore the impact of pressure induced freezing point depression within soils exhibiting strong capillary pressure effect. We solve the coupled mass and energy conservation problem using method of lines (e.g., [3]) with pressure and enthalpy as the primary dependent variables. Strong non-linear coupling develops through the chemical potential equation accounting for coexistence of ice and water in the presence of surface tension [5]. We present a sensitivity analysis showing how freezing point depression evolves within a porous block subject to temperature surface boundary cooling and varied capillary pressures.
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Fu, Hongtao, Sisi Dang, Kena Yang, et al. "Phase Field Simulation of Immiscible CO2 Flooding EOR Mechanisms in Porous Media." In Gas & Oil Technology Showcase and Conference. SPE, 2023. http://dx.doi.org/10.2118/214217-ms.
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Abstract CO2 flooding technology for EOR not only meet the needs of oilfield development, but also solve the problem of carbon emission, which has become a global research hotspot. CO2 flooding includes miscible and immiscible flooding. The advantage of immiscible CO2 flooding is the ability to achieve high recovery in different reservoirs or fluid conditions compared with miscible flooding. But there are no reports about quantitative analysis of immiscible CO2 flooding at the micro level due to the expense and complexity of the experiments. In this paper, the process of immiscible CO2 flooding was simulated based on the Navier-Stokes equation in porous media by COMSOL Multiphysics. An ideal homogeneous rock structure model was established to study the influence of interfacial tension, injection velocity, injection viscosity and gravity on immiscible CO2 flooding. The porosity of the model is 34.7% and the permeability is 36.9mD. The simulation of pressure is 10 MPa and the temperature is 80 ℃. It was found that with the injection of CO2, the contact interface of two phases gradually changes from near-piston flow to non-piston flow under immiscible condition. Decreasing the interfacial tension and increasing the injection velocity significantly change the flow paths of CO2 and increase the sweep area of CO2. The difference between CO2 and oil viscosity is one of the factors influencing the occurrence of fingering. Increasing the viscosity of CO2 injection effectively suppress viscous fingering and improve the sweep effect. Gravity is one of the factors affecting the effect of immiscible CO2 flooding. Phase field simulation was used to study immiscible CO2 flooding for the first time. It was found that increasing the viscosity of CO2 injection could significantly enhance recovery. In order to increase the viscosity of CO2, a thickener can be added to the supercritical CO2. This study provides micro-level theoretical support for the development of process parameters in oilfield, and further provides new ideas for CO2 EOR.