Effect of the stagnation temperature on the normal shock wave

Abstract

When the stagnation temperature increases, the specific heat does not remain constant and start to vary with this temperature. The gas is perfect; its state equation remains always valid, except, it was called by calorically imperfect gas or gas at high temperature. The purpose of this work is to develop a mathematical model for a normal shock wave at high temperature when the stagnation temperature is taken into account, less than the dissociation of the molecules. A generalisation model for a perfect gas for constant heat specific is obtained. 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.

Stagnation Temperature Effect on the Supersonic Flow Around Pointed Airfoils with Application for Air

“…We assume that the state equation of a perfect gas (P = rRT) remains valid, with R = 287.102 J/(kg K). For PG model g = 1.402 is taken [8,9,14].…”

“…The aerodynamics study problems on a numerical way is a relatively new research area. Most previous work either theoretical [1][2][3][4][5][6], or numerical [3,5,[7][8][9][10][11][12][13][14][15][16] or even experimental in wind tunnel [9] on supersonic flows around airfoils are devoted to rounded airfoils at the leading edge, that is to say a development of a detached shock wave at the leading edge. These studies are generally based on the numerical solution of the Euler equations [1][2][3][4][5][6] or the equation of potential speed [1,4,5].…”

Stagnation temperature effect on the supersonic flow around pointed airfoils with application for air

“…We assume that the state equation of a perfect gas (P = rRT) remains valid, with R = 287.102 J/(kg K). For PG model g = 1.402 is taken [8,9,14]. For the determination of the parameters (M 2 , b, T 2 /T 1 , r 2 /r 1 , P 2 /P 1 , P 0 2 /P 0 1 , DS 21 ) through the oblique shock, the HT model presented in references [10][11][12][13] is used after making a correction to the relation between b, c and M 1 , since the authors used the equation designed for the PG model to constant C P [10], given the difficulty of finding an analytic form, which gives results far enough of reality, and that does not meet the need for HT assumptions This equation is the most interesting in the calculation of the shock parameters, since all the other parameters depend on b, c and M 1 .…”

“…Then in this work, we will determine the deviation b with high precision according to the real HT model presented in this work. Since the development of an analytic relation between b, c and M 1 is quite complicated, we will use the relations of a normal shock wave to HT model [14].…”

“…The aerodynamics study problems on a numerical way is a relatively new research area. Most previous work either theoretical [1][2][3][4][5][6], or numerical [3,5,[7][8][9][10][11][12][13][14][15][16] or even experimental in wind tunnel [9] on supersonic flows around airfoils are devoted to rounded airfoils at the leading edge, that is to say a development of a detached shock wave at the leading edge. These studies are generally based on the numerical solution of the Euler equations [1][2][3][4][5][6] or the equation of potential speed [1,4,5].…”