Specific impulse losses due to friction and dispersion in a gas-film cooled liquid rocket engine nozzle

Conclusions The proposed method and program for calculating the compressible turbulent boundary layer in rocket engine nozzles with gas film cooling make it possible to determine the specific impulse losses due to friction, the heat fluxes and other characteristics of the flow. The calculations are based on the numerical solution of the equations of gas dynamics in the boundary layer approximation using a three-parameter differential turbulence model.The calculations for nozzles without film cooling showed that the contours occupying a narrow interval between the families of contours with uniform and variational characteristics have the minimum impulse losses due to friction and dispersion. In contrast to the known results, the loss minimum is displaced relative to nozzles with a variational characteristic (Rao nozzles) towards truncated nozzles with a uniform characteristic.The dependence of the maximum heat transfer to the wall in the critical throat section of the nozzle on the rate of flow of fuel into the film has been determined for nozzles with film cooling. It is shown that as the film flow rate increases, the friction losses decrease, and the minimum of the impulse losses due to friction and dispersion is shifted towards the contours with a variational characteristic, which have the minimum dispersion losses. The total impulse losses, which take into account the change in the fuel component ratio in the flow core due to the diversion of part of the fuel into the film, increase with increase in the film flow rate.The results of our numerical investigation of the effect of the contour shape and film flow rate indicate that the contour with a variational characteristic, which has near-minimum specific impulse losses due to friction and dispersion, should be used as the optimum contour for LRE nozzles.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 82–93, May–June, 1993.deceased.The authors wish to thank their colleagues at the Énergomash NPO L. P. Vereshchak and L. K. Danilyuk for assisting with the calculations, the participants in G. A. Lyubimov's seminar for discussing the results obtained, and D. A. Mel'nikov, U. G. Pirumov, and A. A. Sergienko for valuable advice.     

Uniformization of nonlocal elliptic operators and KK-theory

By a pseudodifferential uniformization of a nonlocal elliptic operator we mean the procedure of reducing the operator to a pseudodifferential operator with a controlled modification of the index. In the paper, we suggest an approach to solving the uniformization problem; this approach uses the reduction of the symbol of a nonlocal operator to the symbol of a pseudodifferential operator. The technical apparatus here is Kasparov’s KK-theory.     

Elliptic expansion–contraction problems on manifolds with boundary

Expansion–contraction boundary value problems on manifolds with boundary are studied. The trajectory symbols of such problems are calculated, an analogue of the Shapiro–Lopatinskii condition is obtained, and the corresponding finiteness theorem is given.     

The eta invariant and parity conditions

We give a formula for the η-invariant of odd-order operators on even-dimensional manifolds and even-order operators on odd-dimensional manifolds. Second-order operators with nontrivial η-invariants are found. This solves a problem posed by Gilkey.     

Some problems of integration in bundles

Translated from Matematicheskie Zametki, Vol. 51, No. 5, pp. 114–124, May, 1992.     

On a Nation of Resurgent Function of Several Variables

The Paper presents the definition of a resurgent a resurgent function of several independent variables. The main properties of the introduced notions are investigated.