Isentropic Approximation of Quasi–One-Dimensional Unsteady Nozzle Flow

2009 ◽  
Vol 41 (4) ◽  
pp. 1693-1712 ◽  
Author(s):  
Shuxing Chen ◽  
Jinbo Geng ◽  
Yongqian Zhang
1960 ◽  
Vol 64 (598) ◽  
pp. 632-635 ◽  
Author(s):  
R. A. A. Bryant

The concept of small stage efficiency is introduced when studying one-dimensional gas flow in nozzles in order to permit a closer approximation of real flow conditions than is possible from an isentropic analysis. It is more or less conventional to assume the flow conditions are adiabatic whenever the small stage efficiency is used. That is to say, small stage efficiency is generally considered in relation to flows contained within adiabatic boundaries, in which case it becomes a measure of the heat generated by internal frictional effects alone.


2019 ◽  
Vol 21 (8) ◽  
pp. 1493-1519
Author(s):  
Abhishek Y Deshmukh ◽  
Carsten Giefer ◽  
Dominik Goeb ◽  
Maziar Khosravi ◽  
David van Bebber ◽  
...  

Direct injection of compressed natural gas in internal combustion engines is a promising technology to achieve high indicated thermal efficiency and, at the same time, reduce harmful exhaust gas emissions using relatively low-cost fuel. However, the design and analysis of direct injection–compressed natural gas systems are challenging due to small injector geometries and high-speed gas flows including shocks and discontinuities. The injector design typically involves either a multi-hole configuration with inwardly opening needle or an outwardly opening poppet-type valve with small geometries, which make accessing the near-nozzle-flow field difficult in experiments. Therefore, predictive simulations can be helpful in the design and development processes. Simulations of the gas injection process are, however, computationally very expensive, as gas passages of the order of micrometers combined with a high Mach number compressible gas flow result in very small simulation time steps of the order of nanoseconds, increasing the overall computational wall time. With substantial differences between in-nozzle and in-cylinder length and velocity scales, simultaneous simulation of both regions becomes computationally expensive. Therefore, in this work, a quasi-one-dimensional nozzle-flow model for an outwardly opening poppet-type injector is developed. The model is validated by comparison with high-fidelity large-eddy simulation results for different nozzle pressure ratios. The quasi-one-dimensional nozzle-flow model is dynamically coupled to a three-dimensional flow solver through source terms in the governing equations, named as dynamically coupled source model. The dynamically coupled source model is then applied to a temporal gas jet evolution case and a cold flow engine case. The results show that the dynamically coupled source model can reasonably predict the gas jet behavior in both cases. All simulations using the new model led to reductions of computational wall time by a factor of 5 or higher.


2013 ◽  
Vol 737 ◽  
pp. 146-175 ◽  
Author(s):  
S. LeMartelot ◽  
R. Saurel ◽  
O. Le Métayer

AbstractExact compressible one-dimensional nozzle flow solutions at steady state are determined in various limit situations of two-phase liquid–gas mixtures. First, the exact solution for a pure liquid nozzle flow is determined in the context of fluids governed by the compressible Euler equations and the ‘stiffened gas’ equation of state. It is an extension of the well-known ideal-gas steady nozzle flow solution. Various two-phase flow models are then addressed, all corresponding to limit situations of partial equilibrium among the phases. The first limit situation corresponds to the two-phase flow model of Kapila et al. (Phys. Fluids, vol. 13, 2001, pp. 3002–3024), where both phases evolve in mechanical equilibrium only. This model contains two entropies, two temperatures and non-conventional shock relations. The second one corresponds to a two-phase model where the phases evolve in both mechanical and thermal equilibrium. The last one corresponds to a model describing a liquid–vapour mixture in thermodynamic equilibrium. They all correspond to two-phase mixtures where the various relaxation effects are either stiff or absent. In all instances, the various flow regimes (subsonic, subsonic–supersonic, and supersonic with shock) are unambiguously determined, as well as various nozzle solution profiles.


1971 ◽  
Vol 93 (4) ◽  
pp. 576-586
Author(s):  
Roa-Ling Wang

An experimental and theoretical study has been made on chemical nonequilibrium flows in a supersonic nozzle for a mixture of dissociated gases and inert diluent. In the calculations, four different flow behaviors were assumed: one-dimensional non-equilibrium, two-dimensional nonequilibrium, two-dimensional equilibrium, and two-dimensional frozen flows. These were compared with measurements of the static pressure and NO2 concentration in the supersonic nozzle flow of the NO2-N4O2-N2 reactive system. Relatively good agreement demonstrates the applicability of the proposed calculation methods and the validity of the assumed reaction mechanisms and their rate constants.


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