Abstract: Numerical modeling of fluid flows, whether compressible or incompressible, laminar or turbulent presents a considerable contribution in the scientific and industrial fields. However, the development of an approximate model of a supersonic flow requires the introduction of specific and more precise techniques and methods. For this purpose, the object of this paper is modeling a supersonic flow of inviscid fluid around a dihedral airfoil. Based on the thin airfoils theory and the non-dimensional stationary Steichen equation of a two-dimensional supersonic flow in isentropic evolution, we obtained a solution for the downstream velocity potential of the oblique shock at the second order of relative thickness that characterizes a perturbation parameter. This result has been dealt with by the asymptotic analysis and characteristics method. In order to validate our model, the results are discussed in comparison with theoretical and experimental results. Indeed, firstly, the comparison of the results of our model has shown that they are quantitatively acceptable compared to the existing theoretical results. Finally, an experimental study was conducted using the AF300 supersonic wind tunnel. In this experiment, we have considered the incident upstream Mach number over a symmetrical dihedral airfoil wing. The comparison of the different Mach number downstream results of our model with those of the existing theoretical data (relative margin between 0.07% and 4%) and with experimental results (concordance for a deflection angle between 1° and 11°) support the validation of our model with accuracy.
Abstract: An analytical investigation is performed to study the unsteady response of a one-dimensional, non-linear dynamic shock system to external downstream pressure perturbations in a supersonic flow in a varying area duct. For a given pressure ratio across a wind tunnel, the normal shock's location can be computed as per one-dimensional steady gas dynamics. Similarly, for some other pressure ratio, the location of the normal shock will change accordingly, again computed using one-dimensional gas dynamics. This investigation focuses on the small-time interval between the first steady shock location and the new steady shock location (corresponding to different pressure ratios). In essence, this study aims to shed light on the motion of the shock from one steady location to another steady location. Further, this study aims to create the foundation of the Unsteady Gas Dynamics field enabling further insight in future research work. According to the new pressure ratio, a pressure pulse, generated at the exit of the tunnel which travels and perturbs the shock from its original position, setting it into motion. During such activity, other numerous physical phenomena also happen at the same time. However, three broad phenomena have been focused on, in this study - Traversal of a Wave, Fluid Element Interactions and Wave Interactions. The above mentioned three phenomena create, alter and kill numerous waves for different conditions. The waves which are created by the above-mentioned phenomena eventually interact with the shock and set it into motion. Numerous such interactions with the shock will slowly make it settle into its final position owing to the new pressure ratio across the duct, as estimated by one-dimensional gas dynamics. This analysis will be extremely helpful in the prediction of inlet 'unstart' of the flow in a supersonic engine intake and its prominence with the incoming flow Mach number, incoming flow pressure and the external perturbation pressure is also studied to help design more efficient supersonic intakes for engines like ramjets and scramjets.
Abstract: The purpose of this work is to simulate the flow at the exit of Vulcan 1 engine of European launcher Ariane 5. The geometry of the propellant nozzle is already determined using the characteristics method. The pressure in the outlet section of the nozzle is less than atmospheric pressure on the ground, causing the existence of oblique and normal shock waves at the exit. During the rise of the launcher, the atmospheric pressure decreases and the shock wave disappears. The code allows the capture of shock wave at exit of nozzle. The numerical technique uses the Flux Vector Splitting method of Van Leer to ensure convergence and avoid the calculation instabilities. The Courant, Friedrichs and Lewy coefficient (CFL) and mesh size level are selected to ensure the numerical convergence. The nonlinear partial derivative equations system which governs this flow is solved by an explicit unsteady numerical scheme by the finite volume method. The accuracy of the solution depends on the size of the mesh and also the step of time used in the discretized equations. We have chosen in this study the mesh that gives us a stationary solution with good accuracy.
Abstract: This paper outlines the development of an
experimental technique in quantifying supersonic jet flows, in an
attempt to avoid seeding particle problems frequently associated with
particle-image velocimetry (PIV) techniques at high Mach numbers.
Based on optical flow algorithms, the idea behind the technique
involves using high speed cameras to capture Schlieren images of the
supersonic jet shear layers, before they are subjected to an adapted
optical flow algorithm based on the Horn-Schnuck method to
determine the associated flow fields. The proposed method is capable
of offering full-field unsteady flow information with potentially
higher accuracy and resolution than existing point-measurements or
PIV techniques. Preliminary study via numerical simulations of a
circular de Laval jet nozzle successfully reveals flow and shock
structures typically associated with supersonic jet flows, which serve
as useful data for subsequent validation of the optical flow based
experimental results. For experimental technique, a Z-type Schlieren
setup is proposed with supersonic jet operated in cold mode,
stagnation pressure of 4 bar and exit Mach of 1.5. High-speed singleframe
or double-frame cameras are used to capture successive
Schlieren images. As implementation of optical flow technique to
supersonic flows remains rare, the current focus revolves around
methodology validation through synthetic images. The results of
validation test offers valuable insight into how the optical flow
algorithm can be further improved to improve robustness and
accuracy. Despite these challenges however, this supersonic flow
measurement technique may potentially offer a simpler way to
identify and quantify the fine spatial structures within the shock shear
layer.
Abstract: Traditional mechanical control systems in thrust
vectoring are efficient in rocket thrust guidance but their costs
and their weights are excessive. The fluidic injection in the nozzle
divergent constitutes an alternative procedure to achieve the goal. In
this paper, we present a 3D analytical model for fluidic injection
in a supersonic nozzle integrating an orifice. The fluidic vectoring
uses a sonic secondary injection in the divergent. As a result, the
flow and interaction between the main and secondary jet has built in
order to express the pressure fields from which the forces and thrust
vectoring are deduced. Under various separation criteria, the present
analytical model results are compared with the existing numerical
and experimental data from the literature.
Abstract: Universal modeling method well proven for industrial
compressors was applied for design of the high flow rate supersonic
stage. Results were checked by ANSYS CFX and NUMECA Fine
Turbo calculations. The impeller appeared to be very effective at
transonic flow velocities. Stator elements efficiency is acceptable at
design Mach numbers too. Their loss coefficient versus inlet flow
angle performances correlates well with Universal modeling
prediction. The impeller demonstrates ability of satisfactory operation
at design flow rate. Supersonic flow behavior in the impeller inducer
at the shroud blade to blade surface Φ des deserves additional study.
Abstract: There is an evident trend to elevate pressure ratio of a
single stage of a turbo compressors - axial compressors in particular.
Whilst there was an opinion recently that a pressure ratio 1,9 was a
reasonable limit, later appeared information on successful modeling
tested of stages with pressure ratio up to 2,8. The authors recon that
lack of information on high pressure stages makes actual a study of
rational choice of design parameters before high supersonic flow
problems solving. The computer program of an engineering type was
developed. Below is presented a sample of its application to study
possible parameters of the impeller of the stage with pressure ratio
3,0. Influence of two main design parameters on expected efficiency,
periphery blade speed and flow structure is demonstrated. The results
had lead to choose a variant for further analysis and improvement by
CFD methods.
Abstract: The aim of this work is to analyze a viscous flow
around the axisymmetric blunt body taken into account the mesh size
both in the free stream and into the boundary layer. The resolution of
the Navier-Stokes equations is realized by using the finite volume
method to determine the flow parameters and detached shock
position. The numerical technique uses the Flux Vector Splitting
method of Van Leer. Here, adequate time stepping parameter, CFL
coefficient and mesh size level are selected to ensure numerical
convergence. The effect of the mesh size is significant on the shear
stress and velocity profile. The best solution is obtained with using a
very fine grid. This study enabled us to confirm that the
determination of boundary layer thickness can be obtained only if the
size of the mesh is lower than a certain value limits given by our
calculations.
Abstract: This work presents a numerical simulation of the interaction of an incident shock wave propagates from the left to the right with a cone placed in a tube at shock. The Mathematical model is based on a non stationary, viscous and axisymmetric flow. The Discretization of the Navier-stokes equations is carried out by the finite volume method in the integral form along with the Flux Vector Splitting method of Van Leer. Here, adequate combination of time stepping parameter, CFL coefficient and mesh size level is selected to ensure numerical convergence. The numerical simulation considers a shock tube filled with air. The incident shock wave propagates to the right with a determined Mach number and crosses the cone by leaving behind it a stationary detached shock wave in front of the nose cone. This type of interaction is observed according to the time of flow.
Abstract: High-velocity oxygen fuel (HVOF) thermal spraying
uses a combustion process to heat the gas flow and coating material.
A computational fluid dynamics (CFD) model has been developed to
predict gas dynamic behavior in a HVOF thermal spray gun in which
premixed oxygen and propane are burnt in a combustion chamber
linked to a parallel-sided nozzle. The CFD analysis is applied to
investigate axisymmetric, steady-state, turbulent, compressible,
chemically reacting, subsonic and supersonic flow inside and outside
the gun. The gas velocity, temperature, pressure and Mach number
distributions are presented for various locations inside and outside
the gun. The calculated results show that the most sensitive
parameters affecting the process are fuel-to-oxygen gas ratio and
total gas flow rate. Gas dynamic behavior along the centerline of the
gun depends on both total gas flow rate and fuel-to-oxygen gas ratio.
The numerical simulations show that the axial gas velocity and Mach
number distribution depend on both flow rate and ratio; the highest
velocity is achieved at the higher flow rate and most fuel-rich ratio.
In addition, the results reported in this paper illustrate that the
numerical simulation can be one of the most powerful and beneficial
tools for the HVOF system design, optimization and performance
analysis.
Abstract: In this work, we try to find the best setting
of Computational Fluid Dynamic solver available for the problems in
the field of supersonic internal flows. We used the supersonic air-toair
ejector to represent the typical problem in focus. There are
multiple oblique shock waves, shear layers, boundary layers
and normal shock interacting in the supersonic ejector making this
device typical in field of supersonic inner flows. Modeling of shocks
in general is demanding on the physical model of fluid, because
ordinary conservation equation does not conform to real conditions in
the near-shock region as found in many works. From these reasons,
we decided to take special care about solver setting in this article by
means of experimental approach of color Schlieren pictures and
pneumatic measurement. Fast pressure transducers were used to
measure unsteady static pressure in regimes with normal shock in
mixing chamber. Physical behavior of ejector in several regimes is
discussed. Best choice of eddy-viscosity setting is discussed on the
theoretical base. The final verification of the k-ω SST is done on the
base of comparison between experiment and numerical results.
Abstract: The aim of this work is to analyze a viscous flow in
the axisymmetric nozzle taken into account the mesh size both in the
free stream and into the boundary layer. The resolution of the Navier-
Stokes equations is realized by using the finite volume method to
determine the supersonic flow parameters at the exit of convergingdiverging
nozzle. The numerical technique uses the Flux Vector
Splitting method of Van Leer. Here, adequate time stepping
parameter, along with CFL coefficient and mesh size level is selected
to ensure numerical convergence. The effect of the boundary layer
thickness is significant at the exit of the nozzle. The best solution is
obtained with using a very fine grid, especially near the wall, where
we have a strong variation of velocity, temperature and shear stress.
This study enabled us to confirm that the determination of boundary
layer thickness can be obtained only if the size of the mesh is lower
than a certain value limits given by our calculations.
Abstract: Supersonic open and closed cavity flows are investigated experimentally and computationally. Free stream Mach number of two is set. Schlieren imaging is used to visualise the flow behaviour showing stark differences between open and closed. Computational Fluid Dynamics (CFD) is used to simulate open cavity of flow with aspect ratio of 4. A rear wall treatment is implemented in order to pursue a simple passive control approach. Good qualitative agreement is achieved between the experimental flow visualisation and the CFD in terms of the expansion-shock waves system. The cavity oscillations are shown to be dominated by the first and third Rossister modes combining to high fluctuations of non-linear nature above the cavity rear edge. A simple rear wall treatment in terms of a hole shows mixed effect on the flow oscillations, RMS contours, and time history density fluctuations are given and analysed.
Abstract: Hypersonic flows around spatial vehicles during their
reentry phase in planetary atmospheres are characterized by intense
aerothermal phenomena. The aim of this work is to analyze high
temperature flows around an axisymmetric blunt body taking into
account chemical and vibrational non-equilibrium for air mixture
species. For this purpose, a finite volume methodology is employed
to determine the supersonic flow parameters around the axisymmetric
blunt body, especially at the stagnation point and along the wall of
spacecraft for several altitudes. This allows the capture shock wave
before a blunt body placed in supersonic free stream. The numerical
technique uses the Flux Vector Splitting method of Van Leer. Here,
adequate time stepping parameter, along with CFL coefficient and
mesh size level are selected to ensure numerical convergence, sought
with an order of 10-8
Abstract: The aim of this work is to determine the supersonic
nozzle profiles used in propulsion, for the launchers or embarked
with the satellites. This design has as a role firstly, to give a
important propulsion, i.e. with uniform and parallel flow at exit,
secondly to find a short length profiles without modification of the
flow in the nozzle. The first elaborate program is used to determine
the profile of divergent by using the characteristics method for an
axisymmetric flow. The second program is conceived by using the
finite volume method to determine and test the profile found
connected to a convergent.
Abstract: This article presents the boundary conditions for the problem of turbulent supersonic gas flow in a plane channel with a perpendicular injection jets. The non-reflection boundary conditions for direct modeling of compressible viscous gases are studied. A formulation using the NSCBC (Navier- Stocks characteristic boundary conditions) through boundaries is derived for the subsonic inflow and subsonic non-reflection outflow situations. Verification of the constructed algorithm of boundary conditions is carried out by solving a test problem of perpendicular sound of jets injection into a supersonic gas flow in a plane channel.
Abstract: Computational study of two dimensional supersonic reacting hydrogen-air flows is performed to investigate the nitrogen effects on ignition delay time for premixed and diffusion flames. Chemical reaction is treated using detail kinetics and the advection upstream splitting method is used to calculate the numerical inviscid fluxes. The results show that just in stoichiometric condition for both premixed and diffusion flames, there is monotone dependency of the ignition delay time to the nitrogen addition. In other situations, the optimal condition from ignition viewpoint should be found using numerical investigations.
Abstract: Supersonic hydrogen-air cylindrical mixing layer is
numerically analyzed to investigate the effect of inlet swirl on
ignition time delay in scramjets. Combustion is treated using detail
chemical kinetics. One-equation turbulence model of Spalart and
Allmaras is chosen to study the problem and advection upstream
splitting method is used as computational scheme. The results show
that swirling both fuel and oxidizer streams may drastically decrease
the ignition distance in supersonic combustion, unlike using the swirl
just in fuel stream which has no helpful effect.