• International Journal of Aeronautical and Space Sciences
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• v.10 no.1
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• pp.1-14
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• 2009

When the stagnation temperature increases, the specific heat does not remain constant and start to vary with this temperature. The gas is perfect, it's state equation remains always valid, except, it was called by gas calorically imperfect or gas at high temperatures. The purpose of this work is to develop a mathematical model for a normal shock wave normal at high temperature when the stagnation temperature is taken into account, less than the dissociation of the molecules as a generalisation model of perfect for constant heat specific. A study on the error given by the perfect gas model compared to our model is presented in order to find a limit of application of the perfect gas model. The application is for air.

• Journal of the Korea Institute of Military Science and Technology
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• v.4 no.2
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• pp.202-214
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• 2001

In this paper the upwind flux difference splitting Navier-Stokes method has been applied to study quasi one-dimensional nozzle flow and axisymmetric sphere-cone($5^{\circ}$) flow for the perfect gas, the equilibrium and the nonequilibrium chemically reacting hypersonic flow. The effective gamma(${ \tilde{\gamma}}$), enthalpy to internal energy ratio was used to couple chemistry with the fluid mechanics for equilibrium chemically reacting air. The influences of the various altitude(30km, 50km) at Mach number(15.0, 20.0) were investigated. The equilibrium shock position was located farthest downstream when compared with those of perfect gas in a quasi one-dimensional nozzle. The equilibrium shock thickness over the blunt body region was much thinner than that of perfect gas shock.

• International Journal of Aeronautical and Space Sciences
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• v.9 no.1
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• pp.1-30
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• 2008

When the stagnation temperature of a perfect gas increases, the specific heats and their ratio do not remain constant any more and start to vary with this temperature. The gas remains perfect; its state equation remains always valid, except, it is named in more by calorically imperfect gas. The aim of this work is to trace the profiles of the supersonic axisymmetric Minimum Length Nozzle to have a uniform and parallel flow at the exit section, when the stagnation temperature is taken into account, lower than the dissociation threshold of the molecules, and to have for each exit Mach number and stagnation temperature shape of nozzle. The method of characteristics is used with the algorithm of the second order finite differences method. The form of the nozzle has a point of deflection and an initial angle of expansion. The comparison is made with the calorically perfect gas. The application is for air.

• International Journal of Aeronautical and Space Sciences
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• v.9 no.2
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• pp.9-17
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• 2008

When the stagnation temperature of the combustion chamber or ambient air increases, the specific heats and their ratio do not remain constant any more, and start to vary with this temperature. The gas remains perfect, except, it will be calorically imperfect and thermally perfect. A new generalized form of the Prandtl Meyer function is developed, by adding the effect of variation of this temperature, lower than the threshold of dissociation. The new relation is presented in the form of integral of a complex analytical function, having an infinite derivative at the critical temperature. A robust numerical integration quadrature is presented in this context. The classical form of the Prandtl Meyer function of a perfect gas becomes a particular case of the developed form. The comparison is made with the perfect gas model for aim to present a limit of its application. The application is for air.

• Journal of computational fluids engineering
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• v.1 no.1
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• pp.123-141
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• 1996

In this paper the upwind flux difference splitting Navier-Stokes method has been applied to study the perfect gas and the equilibrium chemically reacting hypersonic flow over an axisymmetric sphere-cone(5°) geometry. The effective gamma(γ), enthalpy to internal energy ratio was used to couple chemistry with the fluid mechanics for equilibrium chemically reacting air. The test case condition was at altitude(30km) and Mach number(15). The equilibrium shock thickness over the blunt body region was much thinner than that of perfect gas shock. The pressure difference between perfect gas and equilibrium gas was about 3 ∼ 5 percent. The heat transfer coefficient were also calculated. The results were compared with VSL results in order to validate the current numerical analysis. The results from current method were compared well VSL results ; however, not well at near nose. The proper boundary condition and grid system will be studied to improve the solution quality.

• 한국전산유체공학회:학술대회논문집
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• 1995.10a
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• pp.203-212
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• 1995

In this paper the upwind flux difference splitting Navier-Stokes method has been applied to study the perfect gas and the equilibrium chemically reacting hypersonic flow over an axisymmetric sphere-cone($5^{\circ}$) geometry. The effective gamma($\bar{r}$), enthalpy to internal energy ratio was used to couple chemistry with the fluid mechanics for equilibrium chemically reacting air. The test case condition was at altitude(30Km) and Mach number(15). The equilibrium shock thickness over the blunt body region was much thinner than that of perfect gas shock. The pressure difference between perfect gas and equilibrium gas was about $3\sim5$ percent. The skin friction coefficient and heat transfer coefficient were also calculated.

• International Journal of Aeronautical and Space Sciences
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• v.7 no.1
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• pp.13-26
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• 2006

When the stagnation temperature of a perfect gas increases, the specific heat for constant pressure and ratio of the specefic heats do not remain constant any more and start to vary with this temperature. The gas remains perfect: its state equation remains always valid, with exception that it will be named by calorically imperfect gas. The aim of this research is to develop the relations of the necessary thermodynamics and geometrical ratios. and to study the supersonic flow at high temperature. lower than the threshold of dissociation. The results are found by the resolution of nonlinear algebraic equations and integration of complex analytical functions where the exact calculation is impossible. The dichotomy method is used to solve the nonlinear equation. and the Simpson algorithm for the numerical integration of the found integrals. A condensation of the nodes is used. Since. the functions to be integrated have a high gradient at the extremity of the interval of integration. The comparison is made with the calorifcally perfect gas to determine the error made by this last. The application is made for the air in a supersonic nozzle.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.1
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• pp.82-90
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• 2017

The aim of this work is to develop a new computational program to determine the effect of using the gas of propulsion of combustion chamber at high temperature on the shape of the two-dimensional Minimum Length Nozzle giving a uniform and parallel flow at the exit section using the method of characteristics. The selected gases are $H_2$, $O_2$, $N_2$, CO, $CO_2$, $H_2O$, $NH_3$, $CH_4$ and air. All design parameters depend on the stagnation temperature, the exit Mach number and the used gas. The specific heat at constant pressure varies with the temperature and the selected gas. The gas is still considered as perfect. It is calorically imperfect and thermally perfect below the threshold of dissociation of molecules. A error calculation between the parameters of different gases with air is done in this case for purposes of comparison. Endless forms of nozzles may be found based on the choise of $T_0$, $M_E$ and the selected gas. For nozzles delivering same exit Mach number with the same stagnation temperature, we can choose the right gas for aerospace manufacturing rockets, missiles and supersonic aircraft and for supersonic blowers as needed in settings conception.

• Advances in aircraft and spacecraft science
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• v.11 no.2
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• pp.195-213
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• 2024

This article deals with the changes in flow air properties across an oblique shock wave for a real gas. The flow through is investigated to find a general form for oblique shock waves. The main objective of this work will result in the development of a new numerical algorithm to determine the effect of the stagnation pressure on supersonic flow for thermally and calorically imperfect gases with a molecular dissociation threshold, thus giving a better affinity to the physical behavior of the waves. So, the effects of molecular size and intermolecular attraction forces are used to correct a state equation, emphasizing the determination of the impact of upstream stagnation parameters on oblique shock waves. As results, the specific heat pressure does not remain constant and varies with the temperature and density. At Mach numbers greater than 2.0, the temperature rise considerably, and the density rise is well above, that predicted assuming ideal gas behavior. It is shown that caloric imperfections in air have an appreciable effect on the parameters developed in the processes is considered. Computation of errors between the present model based on real gas theory and a perfect gas model shows that the influence of the thermal and caloric imperfections associated with a real gas is important and can rise up to 16%.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.9
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• pp.2431-2442
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• 1994

In this paper the efficient space marching Viscous Shock Layer and Parabolized Navier-Stokes method have been applied to study the complex 3-D hypersonic equilibrium chemically reacting flowfilelds over sphere-cone($10^{\circ}$) vehicle at low angles of attack($0^{\circ}~5^{\circ}), Mach 20, and an altitude of 35km. The current bluntbody/afterbody space marching numerical method predicts the complex flowfields accurately and efficiently even on a small computer. The shock thickness from equilibrium air model is thinner than that from the perfect gas model. The windside wall heat-transfer rate, pressure and skin friction force were increased significantly when compared with those of leeside. The CA, CN, CM were increased almost linearly with the angle of attack in this region. The wall pressure, heat transfer, skin friction and axial force coeffient from equilibrium model were much higher than those from perfect gas model. The center of pressure moved forward with the increase of angle of attack.