EP0515295A1 - Nozzle with internal profile adapted to high-temperature flat-bed tests of specimens or the like. - Google Patents

Abstract

The invention relates to a nozzle with internal profile adapted to high-temperature tests of specimens or the like of "flat plate" type, characterised in that it consists, on the one hand, of an axisymmetric convergent portion (1) and of an axisymmetric throat region (2) and, on the other hand, of a divergent portion (3) with superelliptic cross-section, based on two straight generatrices lying in two perpendicular planes, one the so-called minor axis generatrix (G1), the slope of which is of the order of 1 DEG , and the other the so-called major axis generatrix (G2), the slope of which is of the order of 10 DEG , the downstream ends of the corresponding circular generatrices of the throat region being joined to the said minor axis and major axis generatrices by a curve whose equation is such that the first and second derivatives are continuous and the third derivative is monotonic, with a view to avoiding or reducing problems of recompression and possibly of shock formation. <??>Application in particular to elevated-temperature tests of materials for spacecraft. <IMAGE>

Description

The present invention relates to a so-called "high temperature" nozzle and in particular to a plasma nozzle, the internal profile of which is specially designed to allow tests of the flat board type of test tubes, in particular of materials having to withstand high stresses, in particular thermal stresses. and under pressure.

The invention relates more particularly to the testing of materials intended to constitute the hot parts of spacecraft called upon to face the severe conditions of atmospheric reentry which result in high temperatures (1100 to 1900 ° C.) and low pressures for a period of time. relatively large (about half an hour).

The type of test known as "flat board" consists in placing a test tube made up of a monolithic block or of several elements of one or more materials to be tested, parallel to the jet coming from a nozzle and to be measured at different points of the wall of the specimen or of the assembly the static pressure as well as the temperature for incidences of the wall with respect to the jet of the nozzle ranging from 0 to a few degrees.

These tests are carried out using an installation comprising a plasma generator generating a flow at high temperature, a nozzle disposed downstream of the generator and transforming the flow to adapt it to the desired test conditions, a test chamber into which the nozzle opens and where are installed the devices for presenting the test pieces or the like as well as the various means of measurement essential for the tests, a diffuser for downstream of the chamber intended to recover the flow after it has passed over the test pieces, a heat exchanger to cool the flow and a vacuum system downstream intended to maintain the low pressure level required, for this type in the room.

The particular shape of the test pieces in the "flat board" tests requires a nozzle of appropriate configuration comprising a straight downstream end edge capable of being connected to one of the straight edges of the test piece.

Currently, two types of nozzle are used for tests in "flat board", namely a nozzle called "square tube" and a nozzle called "semi-circular".

The "square tube" nozzle has a divergent whose section, at the outlet, is in fact slightly rectangular with rounded angles, while the semi-circular nozzle is an axisymmetric nozzle whose divergence is reduced by half along a plane containing the axis of the nozzle.

The tests with these types of nozzle are not fully satisfactory because the latter generate at the outlet a very disturbed vortex flow incompatible with the need for tests in "flat board" to have a very good homogeneity of the flow of hot gas in in order to obtain a distribution as uniform as possible of the static pressures and the thermal fluxes on the exposed face of the test piece.

The object of the invention is to propose a hypersonic nozzle intended for this type of test in "flat board", that is to say having at the outlet a flat part and capable of delivering a flow such that at least at right of said flat part the pressure profile is as uniform as possible.

To this end, the subject of the invention is a nozzle with an internal profile suitable for high-temperature tests of test pieces or the like of the "flat board" type, characterized in that it consists, on the one hand, of a converge and of an axisymmetric neck region and, on the other hand, of a divergence of superelliptic section based on two rectilinear generatrices taken in two perpendicular planes, one, called a minor axis, whose slope is around 1 ° and the other, called major axis, whose slope is of the order of 10 °, the downstream ends of the corresponding circular generators of the neck region being connected to said generators of minor and major axes by a curve whose equation is such that the derivatives first and second are continuous and the third derivative is monotonous, in order to avoid or reduce the problems of recompression and possibly of shock formation.

dans laquelle :

• R₁(x) et R₂(x) sont les distances radiales à l'abscisse X desdites génératrices de petit axe et de grand axe respectivement ;
• Y et Z sont les coordonnées d'un point du divergent ;
• N(X) est l'exposant superelliptique, cet exposant présentant une courbe de variation ayant une forme évoluant de façon croissante depuis la valeur 2 jusqu'à une valeur supérieure permettant d'obtenir la planéité recherchée en sortie de tuyère.

Advantageously, said superelliptic section is an equation curve: $${\text{[Y / R₁ (X)] ² + [Z / R₂ (X)]}}^{\text{N (X)}}\text{= 1}$$

in which :

• R₁ (x) and R₂ (x) are the radial distances at the abscissa X of said generators of minor axis and major axis respectively;
• Y and Z are the coordinates of a point of the divergent;
• N (X) is the superelliptic exponent, this exponent exhibiting a variation curve having a shape progressively increasing from the value 2 to a higher value making it possible to obtain the desired flatness at the nozzle outlet.

The superelliptical exponent thus chosen ensures, on the one hand, the desired flatness at the outlet of the nozzle and, on the other hand, a good connection between the divergent and the neck region.

dans lequel A et B sont des constantes et aX + b - ε est l'équation de la génératrice de grand axe après décalage, l'origine des abscisses étant comptée à partir du col, la valeur X₀, abscisse de l'extrémité amont de ladite génératrice, avant décalage, étant choisie et les valeurs ε, X et X₁, abscisse de l'extrémité amont de ladite génératrice, après décalage, étant calculées d'après le polynôme ci-dessus, afin d'assurer la continuité des dérivées première et seconde au point E₀ ainsi que la stricte monotonie de la dérivée troisième entre E₀ et E₁.In order to further improve the connection between the diverging part and the neck region and to ensure that the transition from the axisymmetric geometry of the neck to the superelliptic geometry of the diverging part takes place with the greatest monotony, in particular at the level of the generator of major axis, the latter is offset by a value ε and the curve connecting the upstream ends of said generator respectively before offset (E₀) and after offset (E₁), is determined from a degree 4 polynomial of the type : $$\text{F (X) = A (X-X₁) ⁴ + B (X-X₁) ³ + aX + b - ε}$$

in which A and B are constants and aX + b - ε is the equation of the generator of major axis after shift, the origin of the abscissa being counted from the neck, the value X₀, abscissa of the upstream end of said generator, before shifting, being chosen and the values ε, X and X₁, abscissa of the upstream end of said generator, after shift, being calculated according to the above polynomial, in order to ensure the continuity of the first and second derivatives at the point E₀ as well as the strict monotony of the third derivative between E₀ and E₁.

It is also important, so that the transition from the axisymmetric geometry of the neck to the superelliptic geometry of the divergent takes place with the greatest monotony, that said curve of variation of the superelliptic exponent N (X) has, in addition, properties of continuity of its first and second derivatives at the connection with the axisymmetric surface of the neck and that in particular at the connection point E0 the first and second derivatives are zero.

It is finally preferable that this property of the evolution curve of N (X) is also found at the outlet of the nozzle and that, in general, said variation curve has first and second derivatives substantially zero at both. extreme values of the exponent, being monotonically increasing and presenting an intermediate inflection point.

The invention thus makes it possible to produce a nozzle, the outlet of which has two practically rectilinear parallel edges connected at the ends by two curves approximately in the form of half-ellipses and in which the outlet flow has a great homogeneity characterized by a small variation in the pressure, of the order of 1%, along the flat part.

• Figure 1 représente schématiquement une coupe axiale suivant une génératrice de petit axe (demi-coupe inférieure) et une génératrice de grand axe (demi-coupe supérieure) d'une tuyère selon l'invention ;
• Figure 2 est une vue agrandie du convergent, de la région du col et du début du divergent de la tuyère de la figure 1 ;
• Figure 3 est une vue en perspective plongeante partielle d'un quart de la tuyère, côté sortie ;
• Figure 4 est une vue en perspective d'un quart du divergent ;
• Figure 5 représente trois coupes radiales d'un quart-du divergent de la figure 4 au voisinage de la sortie
• Figure 6 représente quatre coupes radiales d'un quart d'une autre tuyère selon l'invention, et
• Figure 7 est un diagramme illustrant le raccordement entre la région du col de la tuyère et le divergent.

Other characteristics and advantages will emerge from the following description of an embodiment of a nozzle according to the invention, description given by way of example only and with reference to the appended drawings in which:

• Figure 1 schematically shows an axial section along a generator of small axis (lower half-section) and a generator of large axis (upper half-section) of a nozzle according to the invention;
• Figure 2 is an enlarged view of the convergent, the neck region and the start of the diverging nozzle of Figure 1;
• Figure 3 is a partial plunging perspective view of a quarter of the nozzle, outlet side;
• Figure 4 is a perspective view of a quarter of the divergent;
• Figure 5 shows three radial sections of a quarter of the divergent of Figure 4 in the vicinity of the outlet
• FIG. 6 represents four radial sections of a quarter of another nozzle according to the invention, and
• Figure 7 is a diagram illustrating the connection between the region of the nozzle neck and the divergent.

FIGS. 1 to 4 illustrate an embodiment of a nozzle according to the invention comprising a conical convergent 1, a neck 2 of circular section and a divergent 3 very elongated relative to the length of the convergent 1.

The divergent section has a superelliptic section supported by two rectilinear generators taken in two perpendicular planes containing the axis X′X of the nozzle and constituting two planes of symmetry of the latter.

One of these generators, G1, called the minor axis, is in a plane called φ = 0 ° defining the reference plane XY of FIG. 4, while the other generator, G2, called the major axis, is found in the plane called φ = 90 ° defining the XZ reference plane of said figure 4.

Figures 3 and 4 are partial views in the form of meshes of the nozzle of Figures 1 and 2.

The generator G1 has a slope of about 1 ° relative to the axis X′X, while the generator G2 has a slope of the order of 10 °, always relative to the axis X′X.

The outlet section of the nozzle, a quarter of which can be seen in FIG. 3, is delimited by two practically rectilinear and parallel edges (only one being partially represented at 4 in FIGS. 3 and 4) connected at the ends by substantially elliptical curves (5, Figures 3 and 4). For example, the two practically straight edges have a length of between 0.30 and 0.40 m and the minor axis of the outlet section has a length of between 0.05 and 0.08 m.

The nozzle is intended for heat flow tests on flat plates, one of which is shown diagrammatically at 6 in FIG. 1.

These flat plates consist of test pieces of materials to be tested or assemblies, the upper face of which is arranged in the extension of the lower straight edge. nozzle outlet, means being provided to optionally give a slight inclination of said exposed face of the flat plate 6 by lifting the latter around the edge contiguous to the outlet of the nozzle.

These flat test plates are usually 30 cm wide, so the length of the straight outlet edge 4 of the nozzle must be at least 30 cm.

In accordance with the invention, the diverging part 3 has been shaped so as to pass continuously from a circular axisymmetric geometry at the level of the neck 2, to a superelliptic geometry at the nozzle outlet in order to obtain a practically rectilinear outlet edge of sufficient length and with a pressure profile as uniform as possible.

dans laquelle :

• R₁(X) et R₂(X) sont les distances radiales, à l'abscisse X prise à partir du col 2, desdites génératrices G1 et G2 ;
• Y et Z sont les coordonnées d'un point de la section du divergent à l'abscisse X ;
• N(X) est l'exposant superelliptique.

It has been observed that a remarkably uniform pressure profile is obtained by adopting, as a superellipse type curve of any section of the divergent 3, a curve satisfying the equation: $${\text{[Y / R₁ (x)] ² + [z / R₂ (X)]}}^{\text{N (X)}}\text{= 1}$$

in which :

• R₁ (X) and R₂ (X) are the radial distances, at the abscissa X taken from the neck 2, of said generatrices G1 and G2;
• Y and Z are the coordinates of a point in the section of the divergent at the abscissa X;
• N (X) is the superelliptic exponent.

At neck 2, the abscissa X is zero and R₁ (X) = R₂ (X) = radius of neck 2, assigning the value 2 to N (X).

Then by making N (X) evolve progressively towards a high value, for example 10, by forcing it to follow a variation curve having a shape such that it presents first and second derivatives substantially zero at the two extreme values of the exponent, while being monotonous increasing by presenting an intermediate point of inflection, one obtains a section of nozzle which deforms continuously to result in exit in a profile of the type described above and represented in figure 3.

FIG. 5 illustrates three sections of nozzle at three different abscissa of the divergent.

The sections S1, S2 and S3 correspond to a section S1 / section section of the neck 2 equal to 30, 25 and 20 respectively.

A virtually straight part 4 is thus obtained at the outlet of the nozzle. This part is not strictly rectilinear because the exit section is of superelliptic type but one can tend towards an increasingly accentuated flatness by increasing the value of said superelliptic exponent N (X).

In practice, N (X) can be made to evolve between the values 2 and 20, while respecting said evolution curve, which will make it possible to obtain a flatness compatible with the test specifications required for a plasma nozzle.

Furthermore, to avoid problems of recompression and possibly the formation of shocks immediately downstream of the neck 2, it must be ensured, moreover, that the transition from the axisymmetric geometry of the neck 2 to the superelliptic geometry of the diverging part 3 takes place with the greatest monotony. In particular, in the plane φ = 90 ° the passage between the circular generator of the neck 2 and the generator G2 inclined at approximately 10 ° is accompanied by a discontinuity of the second derivatives which could cause possible recompressions.

To avoid this, we will, in accordance with the invention, consider a new generator G′2 shifted from the previous one by a certain value ε and seek a curve F (X) making it possible to connect the circular generator of the neck to the new generator G ′ 2 while ensuring the continuity of the first and second derivatives as well as the monotony of the third derivative.

In Figure 7 there is shown at 7 a circular generator of the neck 2 tangentially connected to a line y = aX + b at point E₀. This line is shifted in the direction of the axis X′X by a distance ε and translated from the point of origin E₀ of abscissa X₀ to the point of origin E₁ of abscissa X₁, so that the connection curve between the point E₀ of line G2 and the point of origin E₁ of line G′2 satisfy the equation: $$\text{F (X) = A (X-X₁) ⁴ + B (X-X₁) ³ + aX + b - ε}$$

In this equation, A and B are constants. The abscissa X₀ being determined by the point of tangency between the generatrix of major axis, before shift, and the corresponding circular generatrix of the neck, the values ε, X and X₁ are calculated from the above equation so as to ensure the continuity of the first and second derivatives at the point EO as well as the strict monotony of the third derivative between the points E₀ and E₁.

It is therefore preferable to take the line G′2 as the long axis generator rather than the line G2. On the other hand, it is not necessary to effect a similar offset on the generator of minor axis G1, given its very slight slope relative to the axis X′X (less than or equal to 1 °) which makes the risks of recompression unlikely.

Furthermore, it is also important, so that the transition from the axisymmetric geometry of the neck to the superelliptic geometry of the divergent is made with the greatest monotony, that said variation curve of the superelliptic exponent N (X) has, in addition , continuity properties of its first and second derivatives at the connection with the axisymmetric surface of the neck and that in particular at the connection point E₀ the first and second derivatives are zero.

It is finally preferable that this property of the evolution curve of N (X) is also found at the outlet of the nozzle and that, in general, said variation curve has first and second derivatives substantially zero at both. extreme values of the exponent, being monotonically increasing and presenting an intermediate inflection point.

Thus one could take, as the variation curve of N (X), a polynomial of degree 5 insofar as the various conditions set out above are satisfied.

Of course, numerous other functions of the same type or of other types satisfying said fixed conditions could also be suitable by ensuring the required properties of continuity of the first and second derivatives of said functions at the connection (E₀) between the divergent 3 and the axisymmetric surface. neck 2 and at the outlet of the nozzle.

It should be noted that the connection zone between the points E₀ and E₁ is very small compared to the total length of the divergent and of the order of a centimeter and that the superelliptical section of the nozzle, in this connection zone, also satisfies the same equation, stated above, as in the downstream part of the divergent.

Nozzles were produced from the above indications having in their outlet section a remarkably homogeneous flow, the relative pressure differences on the flat part 4 remaining less than 1.5%.

Various simulation calculations have been made and have made it possible to verify this excellent flow homogeneity.

A first calculation game was carried out using a non-viscous flow code allowing the calculation of the cervix at chemical and vibrational equilibrium and of the divergent, either at equilibrium, or in imbalance, or in condition frozen. The results show that the flow freezes quickly after the cervix for all test conditions.

Three-dimensional calculations were carried out with the viscous flow code in the case of an ideal gas (γ = 1.4). The agreement with one-dimensional calculations is excellent. The flow in the outlet section is very homogeneous, the relative pressure differences on the flat part remaining less than 1.5%.

Three-dimensional calculations carried out in viscous flow with simulation in perfect gas (γ = 1.2) of a real gas at equilibrium, lead to the same conclusions of a slightly disturbed and homogeneous flow in the outlet section (Δ P / P = 1% along the flat part).

These viscous calculations were completed by imposing on the entry of the convergent an initial vortex simulating that generated by the operation of the plasma generator. The effect of the vortex is canceled by the acceleration of the longitudinal speed and there is a very homogeneous flow in the exit plane (Δ P / P = 1% along the flat part).

Turbulent boundary layer calculations completed and confirmed the previous results. These computations were carried out for various assumptions of flow, either with the balance (γ = 1,2), or fixed (γ = 1,4) and modelizations plate plane and axisymmetric.

A comparison with the hypothesis of a flat plate laminar boundary layer at equilibrium, confirms the existence of a boundary layer whose thickness is a function of the abscissa X, which thus decreases the cross-section of the fluid in the nozzle, which has the effect of increasing the pressure and temperature levels in the non-viscous nucleus.

If it turns out that the thickness of the boundary layer becomes too great at the outlet of the nozzle, taking into account in particular the test specifications of the test pieces, it may be advantageous to reduce the length of the diverging element while increasing the ratio between the outlet section of the nozzle and the neck section, this ratio being for example between 25 and 45, increasing the slope of the generator G1 which can be between 0.75 ° and 1.3 ° as well as that of the generator G′2 which nevertheless remains less than or equal to 10 °, for example between 6 and 10 °.

Taking into account the test conditions of test pieces 6, namely a static pressure between 7.5 mb and 22 mb and a heat flux between 100 Kw / m² and 350 Kw / m² at the wall temperature of 1200 ° K and generating conditions relating to the plasma, namely a reduced enthalpy (Hi / RTo) of between 50 and 135 and a pressure Pi of between 1b and 14b, a nozzle having a divergent length of 0.9 m was designed counted from the neck, with, at the exit, a small axis of 0.07 m and a major axis of about 0.35 m, with a generator of small axis G1 having a slope of 1.3 °, a generator of major axis G′2 having a slope of 7.735 °, with an outlet section / neck section ratio equal to 33.9 for a neck section of 7 cm².

FIG. 6 represents (in quarter section) the outlet S′1 of such a nozzle, in S′2 the section of the diverging part corresponding to a ratio of 9.45 with respect to the section of the neck, in S′3 a report section 2 and at S′4 a circular report section 2.8 produced in the converging part of the nozzle. Sections S′1 to S′4 are taken respectively on the abscissa along the X′X axis of the nozzle of 0.90 m, 0.35 m, 0.07 m and -0.02 m.

The length of the divergent is not a critical value and depends on the dimensions of the test chamber and the test pieces; on the other hand, the values of the slopes of the generators of small axis and of long axis, as well as the ratio output section / section of neck are values characteristics and determinants of the nozzle according to the invention, as well as of course the equations determining the superelliptic sections of the divergent, including in the zone of connection with the axisymmetric region of the neck.

Tests carried out with such a nozzle for different pairs of generating conditions (Pi and Hi / RTo) gave good agreement with the test specifications imposed, with regard to the pressure levels obtained at the nozzle outlet and a satisfactory level for the heat flows to the wall.

Finally, the invention is obviously not limited to the embodiments shown and described above, but on the contrary covers all variants thereof, in particular with regard to the dimensional parameters characteristic of the divergent, in particular the generators of minor axis and of major axis, the length of the diverging portion and the ratio of the outlet section to the section of the neck, which parameters can vary appreciably according to the test specifications in particular, without thereby departing from the scope of the invention.

Claims (7)

Nozzle with internal profile suitable for high temperature tests of test pieces or the like of the "flat board" type, characterized in that it consists, on the one hand, of a convergent (1) and of a region of the neck (2) axisymmetric and, on the other hand, a divergent (3) of superelliptic section supported by two rectilinear generators taken in two perpendicular planes, one (G1), called of small axis, whose slope is of the order of 1 ° and the other (G2), said to be of major axis, the slope of which is of the order of 10 °, the downstream ends of the corresponding circular generatrices of the neck region being connected to said generatrices of minor axis and major axis by a curve whose equation is such that the first and second derivatives are continuous and the third derivative is monotonous, in order to avoid or reduce the problems of recompression and possibly of shock formation. Nozzle according to claim 1, characterized in that said superelliptic section is an equation curve: $${\text{[Y / R₁ (X)] ² + [Z / R₂ (X)]}}^{\text{N (X)}}\text{= 1}$$

in which : - R₁ (X) and R₂ (X) are the radial distances at the abscissa X of said generators of minor axis (G1) and major axis (G2) respectively; - Y and Z are the coordinates of a point of the divergent (3); - N (X) is the superelliptic exponent, this exponent having a variation curve having a shape progressively increasing from the value 2 to a higher value making it possible to obtain the desired flatness at the nozzle outlet. Nozzle according to claim 1 or 2, characterized in that at least the generator of major axis is offset (G′2) by a value ε and the curve connecting the upstream ends of said generator respectively before offset (E₀) and after offset (E₁) is determined from a polynomial of degree 4 of the type: $$\text{F (X) = A (X-X₁) ⁴ + B (X-X₁) ³ + aX + b - ε}$$

in which A and B are constants and aX + b - ε is the equation of the long axis generator (G′2) after shift, the origin of the abscissa being counted from the neck (2), the value X₀ , abscissa of the upstream end of said generator, before shift, being chosen and the values ε, X and X₁, abscissa of the upstream end of said generator, after shift, being calculated according to the above polynomial, so to ensure the continuity of the first and second derivatives at point E₀ as well as the strict monotony of the third derivative between E _O and E₁. Nozzle according to one of claims 1 to 3, characterized in that the variation curve of the superelliptic exponent N (X) has first and second derivatives substantially zero at the two extreme values of the exponent and being monotonically increasing by comprising an intermediate inflection point. Nozzle according to claim 4, characterized in that the variation curve of the superelliptic exponent N (X) is a polynomial of degree 5. Nozzle according to one of claims 1 to 5, characterized in that the superelliptical exponent varies between the values 2 and 20. Nozzle according to one of claims 1 to 6, characterized by the following dimensional values: - divergent superelliptic section based on a generator with a small axis of slope between 0.75 and 1.3 ° and on a generator with a large axis of slope between 6 and 10 °. - ratio of the outlet section to the neck section of between 25 and 45; - outlet section comprising two practically rectilinear parts of length between 0.30 and 0.40 m connected by substantially semi-elliptical curves, the minor axis of the outlet section having a length between 0.05 and 0.8 m.

Images