Hydraulic Analogy for Isentropic Flow Through a Nozzle

2007

The hydraulic analogy existing between the propagation of wavelets at the free surface flow of a liquid and the propagation of acoustic waves in a compressible gas is used to study aerodynamics problems with phenomena at flow around solids at supersonic velocities and aeroacoustic phenomena in supersonic divergent jets. In particular, water level fluctuations, which are proportional to pressure fluctuations in the gas, are measured with an optical fiber and special measuring apparatus. Investigations are carried out on a convergent-divergent (de Laval) nozzle. This phenomenon is linked to the existence of shock-cells in supersonic jets, which are formed in the output of the nozzle. These experimental results will be compared with the results from numerical solution and will be obtained from our own program and from the commercial program CFD Fluent.

2016

Computational Modeling of supersonic flow pattern is one of the greatest challenges in the domain of CFD analyses. One of the primary requirements of compressible flow simulation is to accurately model the inertia force. The compressible flow in a convergent -divergent (CD) nozzle is investigated by using Finite Volume Method (FVM) for solving partial differential equation with a two equation    turbulence model. The paper presents initial steps in numerical analysis of flow, generated by convergent-divergent nozzle with Mach number M = 3.39 at nozzle exit. The numerical simulations of compressible flow passing through a convergent-divergent (CD) nozzle with a fixed geometry are carried out. Moreover, this paper outlines results from simulations of 2-D finite volume solver based on fluent software. Using structured mesh, the RANS equation with    SST turbulent model has been applied. Again, the influence of the turbulence model, differentiation and computational grid to the so...

International Journal for Research in Applied Science & Engineering Technology, 2021

The research paper simulates airflow in a supersonic De Laval nozzle and explores air flow actions isolated from the local area's nozzle. The pressure levels in the input portion of the nozzle (pressure-inlet condition) and the atmospheric output parts (pressure-outlet condition) are used to replicate the current model. The fluid divides the motion of a lambda shock, led to a series of expansion and compression waves; for 1:4 < NPR < 2:4, the estimation shows the probability of an asymmetric flow structure. Computationally obtained asymmetric flow models are compatible with previous theoretical flow visualization studies. The nozzle pressure ratio (NPR) is equivalent to balancing the nozzle's inlet air pressure to the ambient pressure. Thus, the value of the nozzle pressure ratio in the current system is 1.5, and the amount of inlet air pressure and the pressure at the output is equal to the ambient pressure. The data contrast review indicates adequate coordination between the experimental data and the simulation outcomes. The surrounding zone is also affected during the shock wave formation.

Computers & Fluids, 2001

A technique to simulate the¯ow ®eld near a moving material interface is developed for multi-material compressible¯ow, in particular, for compressible gas±water¯ow. This technique can be conveniently applied with a well-established conservative scheme to solve for the regions away from the interface. Material interfaces are captured using the level set technique with minimum or no smearing. To treat wave interaction with the interface, an implicit characteristic method is developed. In this paper, the method is described in detail and tested extensively for several one-dimensional gas±gas and gas±water cases. Application to multi-dimensional shock±free surface interaction and shock±gas bubble interaction are presented in Part II [Liu TG, Khoo BC, Yeo KS. The simulation of compressible multi-medium¯ow. Part II: Applications to 2D underwater shock refraction, submitted for publication]. Ó

Fluid Dynamics, 1979

Chemical Engineering Science, 2008

A two-fluid model for compressible flow of gas bubbles dispersed in liquid moving through a convergent-divergent nozzle, which is used for a gas-assisted atomization, is presented. The model is developed for flows with high values of the gas volume fraction-up to the phase inversion values. Drag and virtual mass forces are considered. A new method is proposed to correct the virtual mass coefficient for the high bubble loadings. The mixture k-turbulence model is adapted for the nozzle flow. The particle number density equation is solved to calculate the distribution of the locally averaged bubble diameter. Curvilinear body fitted grids are utilized to represent the nozzle shape accurately. It is shown that for numerical stability it is necessary to discretize implicitly the virtual mass term and solve the momentum equations for two phases simultaneously in a coupled way. The comparison between the experimentally measured and the predicted pressure profiles along the nozzle wall demonstrated good overall agreement. Gravitational effects are analysed by modelling a three-dimensional case. The examination of the flow through the nozzle reveals the non-uniformities of the bubble size and volume fraction distributions. It is confirmed that the virtual mass force plays a major role in accelerating/decelerating flows with a relatively low interfacial drag.

SIAM Journal on Applied Mathematics, 2013

Steady, irrotational flow of a compressible fluid through a two-dimensional planar and axisymmetric nozzle is formulated and solved numerically in the hodograph or velocity plane. The Legendre potential is used to express the governing equation which for planar flow is linear and for axisymmetric flow nonlinear. The hodograph transformation method is extended to solve the nozzle problem for supersonic flow. A rectangular numerical domain for the supersonic case results from the way the information travels in the region that is the image of the flow that occurs around the lip of the nozzle surface. Knowledge of the characteristic's exact location in the supercritical region of the domain is not required, but only the general direction in which information propagates.

Advanced Materials Research, 2012

Water production is controlled by the size and distribution of water saturation around wells. A recent discovery shows that not employing hydrodynamic mixing in numerical simulators may underestimate the water transition zone (Duan and Wojtanowicz 2006). This paper reports continuing research into mechanisms causing expansion of the water-saturation transition zone (transverse dispersion) in a segregated flow of oil and water approaching a vertical well's completion. The mechanisms-including nonlinear flow, turbulence, shear rate, and flow baffling at grains-all contribute to the instability of the oil/water interface, resulting in hydrodynamic mixing. Interface instability because of shearing rate has been demonstrated in our recent study on the Hele-Shaw model (Duan and Wojtanowicz 2007). In this paper, we mathematically model the effect of flow baffling and demonstrate transverse dispersion experimentally using a linear physical sandpack. A simple model of tortuous flow was developed to demonstrate the effect of two-phase-flow baffling in granular porous media. The model shows that the change in flow momentum of the two fluids at the point of collision with rock grains becomes the major factor causing water dispersion. A series of segregated-flow runs (top, oil; bottom, water) was carried out using a physical model packed with different porous media at a constant pressure drop. The runs were videotaped and analyzed for saturation distribution using a color-intensity-recognition software. The results clearly demonstrate onset of transverse dispersion of water into the flowing oil. Further dispersion, however, was overshadowed by the dimensional and end-point effects of the model. With a numerical estimation procedure, the initial dispersion rate-computed from the 1D flow model-is the essential data needed to estimate total dispersion in radial inflow to wells.

41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference &amp; Exhibit, 2005