Introduction to "To the Question of Energy Use of Detonation Combustion" By Ya. B. Zel'dovich
Ya. B. Zel’dovich (1914–1987) made numerous contributions [1] to the theory of detonation, beginning with his very well known and widely translated article [2] on detonation structure that first introduced the standard Zel’dovich-von Neumann-Doring (ZND) model of shock-induced combustion. Even at that early stage of detonation research, Zel’dovich was also considering the application of detonations to propulsion and power engineering. He published these ideas in another paper [3] that has been virtually unknown in the West and has apparently remained untranslated until now. We are indebted to Sergey Frolov of the N.N. Semenov Institute of Chemical Physics for first bringing this article to our attention. We believe that the focus of this paper, which is the application of detonation waves to power generation and propulsion, is very relevant to the current activity on pulse detonation engines. In particular, Zel’dovich was apparently the first researcher to consider the questions of the relative efficiency of various combustion modes, the role of entropy production in jet propulsion, and the distinction between unsteady and steady modes of detonation in power engineering and propulsion applications. Even 60 years later, we believe that his results are relevant and can be of value in modern discussions on thermodynamic cycle analysis of detonation waves for propulsion [4]. For these reasons, we have arranged for the paper to be translated and suggested that it be published by the Journal of Propulsion and Power.
To the question of energy use of detonation combustion
D URING detonation combustion1 of explosive gas mixtures, immediately after the passing of detonation wavefront (completion of chemical reaction), the products of combustion are in a state (call it state D) that is quite rich in both heat and kinetic energy (i.e., the energy of translational motion). Assuming no losses, the state D of combustion products can be calculated using the classical thermodynamic theory of Jouguet. The propagation speed of detonation obtained in this calculation agrees well with experiment, which confirms the correctness of the thermodynamic theory as the limiting case with no losses. For the combustion products in the detonation wave, such a calculation gives: density is 2–1.7 times greater than that of the initial mixture (approximately (k + 1)/k times greater, where k is the adiabatic exponent, pvk = const, for the combustion products); pressure is approximately 2 times greater than the pressure achieved in a closedvolume explosion; temperature is 10-20% higher than the temperature of a closed-volume explosion (approximately 2k/(k + 1) times higher); speed of translational motion is about 0.4–0.5 times that of detonation propagation, which means that kinetic energy of translational motion reaches 17% of the total energy of the mixture. It is interesting to consider to what extent detonation combustion of fuel allows more efficient energy use. One often comes across proposals for detonation regime of combustion in machines such as a gas turbine. Below we present a thermodynamic analysis of the efficiency of cycles with detonation. We will consider here the essential aspects and only briefly comment about technical viability of cycles, losses that reduce the efficiency as compared to the calculated values, etc.
Thermal-mechanical fully coupled analysis of high-speed angular contact ball bearings
The thermal and mechanical properties of angular contact ball bearings are critical to their operating accuracy and service life. On the basis of the theory of dynamics and frictional heat generation, this work establishes a thermal-mechanical fully coupled model. The high-speed motion characteristics, temperature, and dynamic stiffness are analyzed, and the simulation results are compared with the theoretical calculation and experimental results. Then, the temperature and axial deformation of the bearings under different rotation speeds are analyzed, and the laws of mechanical and thermal characteristics of the bearings are obtained. Results show that an increase in the rotation speed of the inner ring causes the temperature of each component to increase, with the contact area of the balls showing the greatest increase in temperature. An increase in rotation speed also increases the axial deformation of the inner ring.