scholarly journals Modelling of transcritical and supercritical nitrogen jets

2017 ◽  
Vol 169 (2) ◽  
pp. 125-132
Author(s):  
Eduardo ANTUNES ◽  
Andre SILVA ◽  
Jorge BARATA
Keyword(s):  
Gas Turbines ◽  
Internal Combustion Engines ◽  
Fuel Injection ◽  
Stokes Equations ◽  
Variable Density ◽  
Navier Stokes ◽  
Rocket Engines ◽  
Supercritical Conditions ◽  
Potential Core

The present paper addresses the modelling of fuel injection at conditions of high pressure and temperature which occur in a variety of internal combustion engines such as liquid fuel rocket engines, gas turbines, and modern diesel engines. For this investigation a cryogenic nitrogen jet ranging from transcritical to supercritical conditions injected into a chamber at supercritical conditions was modelled. Previously a variable density approach, originally conceived for gaseous turbulent isothermal jets, imploying the Favre averaged Navier-Stokes equations together with a “k-ε” turbulence model, and using Amagats law for the determination of density was applied. This approach allows a good agreement with experiments mainly at supercritical injection conditions. However, some departure from experimental data was found at transcritical injection conditions. The present approach adds real fluid thermodynamics to the previous approach, and the effects of heat transfer. The results still show some disagreement at supercritical conditions mainly in the determination of the potential core length but significantly improve the prediction of the jet spreading angle at transcritical injection conditions.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

Leading Edge Film Cooling: Computations and Experiments Including Density Effects

1996 ◽  
Author(s):  
Pingfan He ◽  
Dragos Licu ◽  
Martha Salcudean ◽  
Ian S. Gartshore
Keyword(s):  
Experimental Data ◽  
Film Cooling ◽  
Stokes Equations ◽  
Leading Edge ◽  
Variable Density ◽  
Navier Stokes ◽  
Cooling Effectiveness ◽  
Stagnation Line ◽  
Film Cooling Effectiveness ◽  
Blowing Ratio

The effect of varying coolant density on film cooling effectiveness for a turbine blade-model was numerically investigated and compared with experimental data. This model had a semi-circular leading edge with four rows of laterally-inclined film cooling orifices positioned symmetrically about the stagnation line. A curvilinear coordinate-based CFD code was developed and used for the numerical investigation. The code used a domain segmentation strategy in conjunction with general curvilinear grids to model the complex blade configuration. A multigrid method was used to accelerate the convergence rate. The time-averaged, variable-density, Navier-Stokes equations together with the energy or scalar equation were solved. Turbulence closure was attained by the standard k–ε model with a near-wall k model. Either air or CO2 was used as coolant in three cases of injection through single rows and alternatively staggered double raws of holes. Two different blowing rates were investigated in each case and compared with experimental data. The experimental results were obtained using a wind tunnel model, and the mass/heat analogy was used to determine the film cooling effectiveness. The higher density of the carbon dioxide coolant (approximately 1.5 times the density of air) in the isothermal mass injection experiments, was used to simulate the effects of injection of a colder air in the corresponding adiabatic heat transfer situation. Good agreement between calculated and measured film cooling effectiveness was found for low blowing ratio M ≤ 0.5 and the effect of density was not significant. At higher blowing ratio M > 1 the calculations consistently overpredict the measured values of film cooling effectiveness.

scholarly journals Performance investigation of a volute porous tongue of a turbocharger turbine

2020 ◽  
Vol 40 (1) ◽  
pp. 59-66
Author(s):  
Abderrahmane Chachoua ◽  
Mohamed Kamal Hamidou ◽  
Mohammed Hamel
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Gas Turbines ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Recirculation Flow ◽  
Recirculating Flow ◽  
Show Evidence ◽  
The Right

The design for better performance of the spiral housing volute used commonly in radial and mixed inflow gas turbines is of prime importance as it affects the machine stage at both design and off design conditions. The tongue of the scroll divides the flow into two streams, and represents a severe source of disturbances, in terms of thermodynamic parameter uniformity, maximum kinetic energy, the right angle of attack to the rotor and minimum losses. Besides, the volute suffers an undesirable effect due to the recirculating mass flow rate in near bottom vicinity of the tongue. The present project is an attempt to design a tongue fitted with cylindrical holes traversing normal to the stream wise direction, where on account of the large pressure difference between the top and the bottom sides of the tongue will force the recirculating flow to go through the rotor inlet. This possibility with its limitations has not yet been explored. A numerical simulation is performed which might provide our suitable objectives. To achieve this goal the ANSYS code is used to build the geometry, generate the mesh, and to simulate the flow by solving numerically the averaged Navier Stokes equations. Apparently, the numerical results show evidence of favorable impact in using porous tongue. The realization of a contact between the main and recirculation flow by drilled holes on the tongue surface leads to a flow field uniformity, a reduction in the magnitude of the loss coefficient, and a 20 % reduction in the recirculating mass flow rate.

scholarly journals New variational principles for locating periodic orbits of differential equations

2011 ◽  
Vol 369 (1944) ◽  
pp. 2211-2218 ◽  
Author(s):  
Bruce M. Boghosian ◽  
Luis M. Fazendeiro ◽  
Jonas Lätt ◽  
Hui Tang ◽  
Peter V. Coveney
Keyword(s):  
Periodic Orbits ◽  
Variational Principles ◽  
Stokes Equations ◽  
Iterative Algorithms ◽  
Navier Stokes ◽  
Unstable Periodic Orbits ◽  
Navier Stokes Equations ◽  
New Methods ◽  
Discrete Representations

We present new methods for the determination of periodic orbits of general dynamical systems. Iterative algorithms for finding solutions by these methods, for both the exact continuum case, and for approximate discrete representations suitable for numerical implementation, are discussed. Finally, we describe our approach to the computation of unstable periodic orbits of the driven Navier–Stokes equations, simulated using the lattice Boltzmann equation.

NUMERICAL ANALYSIS OF A TWO PHASE FLOW MODEL

2012 ◽  
Vol 09 (03) ◽  
pp. 1250036 ◽  
Author(s):  
MOHAMED ABDELWAHED ◽  
MOHAMED AMARA
Keyword(s):  
Stokes Equations ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Time Discretization ◽  
Variable Density ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Quality Of Water ◽  
Coupling Characteristics

Due to ever increasing water demand, the preservation of water quality is becoming a very important issue. Eutrophication is amongst the particular problems threatening the quality of water. This paper begins with presenting a mathematical model for aeration process in lake used to combat water eutrophication. Two phases are numerically simulated to study the injected air effect on water by using a corrected one phase model described by Navier–Stokes equations with variable density and viscosity representing the mixture. This model is numerically studied by coupling characteristics scheme for time discretization and mixed finite element method for space approximation. An error estimates in space and time for the velocity are obtained. Numerical results are given firstly in support of the mathematical analysis and secondly to simulate a real application case of the studied problem.

scholarly journals Dynamics of a contracting fluid compound filament with a variable density ratio

2021 ◽  
Vol 24 (2) ◽  
pp. first
Author(s):  
Truong V. Vu ◽  
Vinh T. Nguyen ◽  
Phan H. Nguyen ◽  
Nang X. Ho ◽  
Binh D. Pham ◽  
...  
Keyword(s):  
Interfacial Tension ◽  
Stokes Equations ◽  
Weighting Function ◽  
Density Ratio ◽  
Variable Density ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Front Tracking Method ◽  
Fixed Grid ◽  
Eulerian Grid

Introduction: Compound fluid filaments appear in many applications, e.g., drug delivery and processing or microfluidic systems. This paper focuses on the numerical simulation of an incompressible, immiscible, and Newtonian fluid for the contraction process of a fluid compound filament by solving the Navier-Stokes equations. The front-tracking method is used to solve this problem, which uses connected segments (Lagrangian grid) that move on a fixed grid (Eulerian grid) to represent the interface between the liquids. Methods: The interface points are advected by the velocity interpolated from those of the fixed grid using the area weighting function. The coordinates of the interface points are used to construct the indicators specifying the different fluids and compute the interfacial tension force. Results: The simulation results show that under the effects of the interfacial tension, the capsuleshaped filament can transform into a spherical compound droplet (i.e., non-breakup) or can break up into smaller spherical compound and simple droplets (i.e., breakup). When the density ratio of the outer to middle fluids increases, the filament changes from non-breakup to breakup upon contraction. Conclusion: Increasing the density ratio enhances the breakup of the compound filament during contraction. The breakup is also promoted by increasing the initial length of the filament.

scholarly journals Calculation of Pressure Pulsations in the Flow Part of the First Stage of an Axial Turbine in the Rotor-Stator Interaction Zone

2021 ◽  
Vol 320 ◽  
pp. 04011
Author(s):  
S. F. Timushev ◽  
A. V. Kondratov
Keyword(s):  
Gas Turbines ◽  
Stokes Equations ◽  
Stationary Regime ◽  
Turbine Rotor ◽  
Calculation Model ◽  
Rocket Engines ◽  
Interaction Zone ◽  
Pressure Pulsations ◽  
High Resource ◽  
Axial Clearance

A serious problem in the development of reusable liquid-propellant rocket engines (LRE) is the provision of a high resource and reliability of gas turbines of turbopump, which supply fuel to the combustion chamber. This problem can be solved by reducing the level of pressure pulsations in the interaction zone of the turbine rotor-stator and dynamic loads acting on the working and stator blades. In this regard, a useful tool is the method of numerical simulation of the unsteady turbulent flow of a compressible gas in the turbine flow path with the determination of the amplitude of pressure pulsations in the axial clearance between the stator and rotor blade cascades. The calculation model includes the Navier-Stokes equations and equation of energy. Density, thermal conductivity and diffusion coefficient are linearly dependent on temperature and concentration. Calculations were performed on different meshes, proving the mesh convergence of the method upon reaching the quasi-stationary regime. The calculation results show that the pressure pulsations vary greatly with the axial clearance, and the main frequency of the pressure pulsations in the spectrum is the blade passing frequency. The frequency of dynamic moment acting on the blade also coincides with the indicated frequency.

Role of Inlet Boundary Conditions on Fuel-Air Mixing at Supercritical Conditions

2020 ◽  
Author(s):  
Zachary Harris ◽  
Joshua Bittle ◽  
Ajay Agrawal
Keyword(s):  
Experimental Data ◽  
Boundary Conditions ◽  
Gas Turbines ◽  
Alternative Fuels ◽  
Fuel Injection ◽  
Fluid Dynamic ◽  
Supercritical Conditions ◽  
Complex Interactions ◽  
Significant Research ◽  
Air Mixing

Abstract Advanced engine design and alternative fuels present the possibility of fuel injection at purely supercritical conditions in diesel engines and gas turbines. The complex interactions that govern this phenomenon still need significant research for reliable modeling efforts. Boundary conditions for fuel injection are critical to accurate simulation. However, the flow inside the injector itself is often omitted to reduce the computational efforts, and thus, velocity, mass flux, or total pressure is specified at the injector exit (or domain inlet), often with an assumed top hat profile and assumed turbulence levels. Past studies have shown that such simplified inlet boundary treatment has minimal effects on the results for fuel injection in the compressed liquid phase. However, the validity of this approach at supercritical fuel injection conditions has not been assessed so far. In this study, comprehensive real-gas and binary fluid mixing models have been implemented for computational fluid dynamic (CFD) analysis of fuel-air mixing at supercritical conditions. The model is verified using prior CFD results from the literature. Next, the model is used to investigate the effects of the shape of axial velocity and mass fraction profiles at the inlet boundary with the goal to improve the comparison of predictions to experimental data. Results show that the boundary conditions have a significant effect on the predictions, and none of the cases match precisely with experimental data. The study reveals that the physical location of the inlet boundary might be difficult to infer correctly from the experiments and highlights the need for high-quality, repeatable measurements at supercritical conditions to support the development of relevant high-fidelity models for fuel-air mixing.

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