TEMPERATURE MEASUREMENT OF CRYOGENIC NITROGEN JETS AT SUPERCRITICAL PRESSURE

The temperatures of transcritical and supercritical nitrogen jets were measured to explore the in§uence of ¤pseudovaporization¥ upon cryogenic propellant mixing in high-pressure rocket chambers. Pseudovaporization is the large thermodynamic transition near the pseudocritical temperature under transcritical conditions, which can include a drastic density change and large peak of isobaric speci¦c heat. A decline in the rise of temperature along the jet centerline of the transcritical jet was caused at the position where the local temperature reached nearpseudocritical temperature. This can be considered to be due to the large peak of isobaric speci¦c heat. The density jump appeared near the pseudocritical temperature, which can be correlated to the sudden expansion due to pseudovaporization. The axial pro¦les of the temperature and density of the supercritical jet monotonically increased and decreased, respectively, in the downstream region of the end of the jet potential core. Similar to the axial pro¦les, the radial pro¦les of the temperature were in§uenced by the pseudovaporization ¡ i. e., the temperature rise in the radial direction became very shallow in the region where the local temperature was still lower than the pseudocritical temperature. The full width at half maximum of the density pro¦les stayed almost constant further downstream of the end of the jet potential core, whereas that of the mass fraction pro¦les of the incompressible variable-density jet began to increase near the end of the potential core. Hence, the evolutions of jet mixing layers of transcritical jets and variable-density jets can be considered to di ̈er due to pseudovaporization.


INTRODUCTION
Propellant mixing phenomena in liquid rocket combustors are important in the sense that they have a signi¦cant impact on the combustor performance.In particular, most liquid rocket engines used in the ¦rst stage of launch vehicles operate at a pressure above the critical pressure of oxygen.Hence, understanding of the mixing processes involved in cryogenic jets under supercritical pressures is necessary.Figure 1 illustrates the thermodynamic phase diagram of oxygen using pressure and temperature.The arrow in Fig. 1 schematically shows the thermodynamic change of oxygen in such high-pressure rocket combustors.Cryogenic oxygen at an initially subcritical temperature is injected into an environment that exceeds the critical pressure and temperature (5.04 MPa and 154.6 K, respectively).The thermodynamic change from subcritical temperature to supercritical temperature under supercritical pressures is called ¤transcritical¥ [1].The pseudocritical temperatures under transcritical conditions correspond to the boiling temperatures at subcritical pressures.At pseudocritical temperatures, oxygen experiences a large thermodynamic transition from liquid-like properties to gas-like properties, such as a large density change and considerable amount of expansion heat.This large thermodynamic transition is referred to ¤pseudova-porization¥ or ¤pseudoboiling¥ [2].Most studies on §uid mixing under supercritical pressures considered often only the gas-like properties of supercritical §uids, such as the diminishment of gasliquid surface tensions; however, the fact that pseudovaporization is involved in §uid mixing phenomena is also important.
Several numerical studies on transcritical jets have been reported in the last decade [36].Hosangadi et al. [4] simulated cryogenic nitrogen/gaseous nitrogen coaxial jets under transcritical conditions by means of a hybrid large-eddy sim-Figure 1 Schematic of thermodynamic state of oxygen in liquid rocket combustors ulation (LES) / Reynolds-averaged NavierStokes (RANS) simulation method.They suggested that pseudovaporization in §uences the unsteady behavior of the cryogenic jet core.Zong and Yang [3] and Jarczyk and P¦tzner [6] conducted LES of cryogenic nitrogen jets under transcritical conditions.They showed that strong anisotropy of turbulence occurs in the initial mixing region owing to the large density strati¦cation between the injected and ambient §uids.
Quantitative measurement data of transcritical jets are indispensable for both validation of these numerical studies and better understanding of mixing phenomena.However, only a few sets of quantitative experimental data have been made public compared with data on incompressible variable-density jets [7].To the best of the authors£ knowledge, Raman-scattering-based density pro¦les of transcritical nitrogen jets are the only quantitative data that have been published [1,8].These pro¦les showed that the spatial growth rate of transcritical jets agrees with those predicted by the theoretical equations and measurements for incompressible variable-density turbulent jets.However, the jet temperature at the injector exit almost reaches the pseudocritical temperature; so, pseudovaporization may only in §uence the region close to the injector.In addition, the error of the Raman scattering measurement in high-pressure environments becomes large because scattering due to the high-density ambient §uids weakens the signals of the jets [9].
The purpose of this study was to explore the in §uence of pseudovaporization upon jet mixing by using quantitative data on transcritical jets.High-pressure injection tests were conducted and temperature pro¦les of a transcritical nitrogen jet were obtained by means of a temperature sensor traverse.For comparison, temperature pro¦les of a supercritical nitrogen jet at a temperature over the pseudocritical temperature were also measured.

Experimental Setup
In the experiment, cryogenic nitrogen was employed as an injectant because nitrogen is thermodynamically similar to oxygen.The critical pressure, temperature, and density of nitrogen are 3.4 MPa, 126.2 K, and 313.3 kg/m 3 , respectively.
Figure 2 shows a schematic diagram of the experimental setup.The test stand comprises an injector, high-pressure chamber, and supply system for the cryogenic nitrogen.Cryogenic nitrogen is ¦rst pressurized to the required level by high-pressure nitrogen gas in an LN 2 pressurized reservoir and then injected at a cryogenic temperature into the high-pressure chamber.The high-pressure chamber is ¦lled with nitrogen gas at a supercritical pressure and ambient temperature.The injector is placed in the top §ange of the high-pressure chamber.Figure 3 shows the injector details.The injector has an outer nozzle to blow a co §ow jet.This paper only presents the results of a round jet from the inner nozzle.The injector is about half the size of practical rocket engine injectors.
The temperature of the cryogenic nitrogen is controlled using an electronic heater installed in the reservoir as shown in Fig. 2b.The injector is not insulated, but the injector is carefully cooled prior to injection so that the temperature of the nitrogen at the injector exit is maintained within ±0.9 K of the target value.

Test Conditions
The temperature pro¦les of cryogenic nitrogen jets were measured under two di¨erent §ow conditions: transcritical and supercritical.Table 1 summarizes the §ow conditions.The ambient pressure of 4.0 MPa corresponds to 1.18 times of the critical pressure of nitrogen.The pseudcritical temperature at this pressure is approximately 129.7 K.The present jet temperature of the transcritical case was about 27 K below the pseudocritical temperature; so, the in §uence of pseudovaporization would be observed downstream of the jet core, not only in the region close to the injector exit.
Figure 4 shows the density, speci¦c enthalpy, and isobaric speci¦c heat of nitrogen at 4.0 MPa.The pseudocritical temperature exists between the injection temperature of cryogenic nitrogen and the ambient gaseous nitrogen in the transcritical case.In the vicinity of the pseudocritical temperature, density greatly  changes and there is a signi¦cant change in the speci¦c enthalpy.This large enthalpy change is similar to the latent heat of vaporization at subcritical pressures.Hence, a large peak of isobaric speci¦c heat appears at the pseudocritical temperature.On the other hand, the supercritical jet does not experience this large thermodynamic transition.

Measurement
Time-averaged backlit images were obtained to compare the §ow ¦eld features of the transcritical and supercritical jets.A temperature sensor probe was mounted on a two-axis traversing device installed downstream of the injector as shown in Fig. 5.This ¦gure also describes the coordinates for the temperature measurement.For the transcritical jet, the axial temperature pro¦le was measured by a NETSUSHIN 0.5-millimeterdiameter platinum resistance temperature sensor; the radial temperature pro¦le, where spatial resolution is more Figure 5 Temperature measurement probe important, was measured with a 0.25-millimeter-diameter K-type thermocouple.For the supercritical jet, the axial and radial temperature pro¦les were measured with a 0.25-millimeter-diameter K-type thermocouple.
The temperature sensors were calibrated against a high-accuracy Cernox sensor and the measurement accuracy of the platinum resistance sensor was evaluated to be ±0.3K.The uncertainty for the thermocouple was much larger but has not been quanti¦ed at present.The §ow rate of the cryogenic nitrogen was measured at an ori¦ce inserted just upstream of the run valve.

Visualization
Figure 6 illustrates the time-averaged backlit pictures of the transcritical and supercritical jets.A dark core region of the transcritical jet was clearly observed and had a length of about 20D from the injector exit.In contrast, the shadow of the supercritical jet seemed fainter shorter than the dark core of the transcritical jet.

Axial Pro¦les
Figure 7 shows the axial pro¦les and axial gradients of the temperature along the jet centerline.The temperature pro¦le of the transcritical jet can be divided into four regions: (I) a jet potential core region with almost constant temperature (0 < x/D < 5); (II) linear increase at 5 < x/D < 15; (III) very shallow increase near x/D = 15; and (IV) linear increase again with a larger gradient at x/D > 20.A decline in the rise of temperature appeared where the local temperature reached near-pseudocritical temperature; hence, it can be considered to be due to the large isobaric speci¦c heat near the pseudocritical temperature as described in Fig. 4c.On the other hand, the temperature pro¦le of the supercritical jet did not have the region with a shallow temperature gradient after the end of the jet potential core.The di¨erence of the temperature gradients of the transcritical and supercritical jets are also observed in Fig. 7c.Figures 8a and 8b plot the axial pro¦les of the normalized density.The jet density was calculated from the jet temperature at the constant pressure of 4.0 MPa because both the transcritical and the supercritical jets had su©ciently low Mach numbers to be regarded as incompressible §ows.For comparison, the mass fraction pro¦les were also plotted for an incompressible variabledensity CO 2 jet in air as measured by Cheng and Rodi [7].The density of the supercritical jet decayed in the curve in a similar manner to that of the incompressible variable-density jet downstream of the end of the jet potential core.For the transcritical jet, the density jump appeared at the position where the local temperature was equal to the pseudocritical temperature.Similar to the unique pro¦le of the jet temperature in this region, it can be correlated to the sudden expansion due to pseudovaporization.To clarify, the axial gradient of the normalized density and mass fraction are plotted in Fig. 8c.The gradient of the transcritical jets near x/D = 15 is signi¦cantly lower than those of the supercritical and incompressible variable-density jets. of the transcritical jet temperature several axial distances from the injector exit.In the radial pro¦les at the positions where the jet centerline temperature did not reach the pseudocritical temperature (at x/D < 20), the temperature gradients in the radial direction in the region where the local temperature was still lower than the pseudocritical temperature (at |r/D| < 1) are shallower than those at |r/D| > 1.Hence, the in §uence of pseudovaporization also appeared in the radial pro¦les of the temperature.The temperature gradients at |r/D| < become small as the layer develops.Once the jet centerline temperature exceeded the pseudocritical temperature (at x/D = 35), the decrease of the rise in temperature was no longer observed and the pro¦le became similar to a Gaussian distribution.
Figure 10 shows the axial evolution of the full width at half maximum (FWHM) of the radial temperature and density pro¦les.The FWHM of density was determined by the radial pro¦les of the nondimensional density as calculated from the temperature at a constant pressure of 4.0 MPa.The FWHM of density stayed almost constant further downstream of the end of the jet potential core (0 < x/D < 15), whereas that of temperature immediately increased downstream of the injector exit.Note that the FWHM of the mass fraction pro¦les of the incompressible variable-density CO 2 jet began to increase near the end of the jet potential core.Hence, the evolutions of the jet mixing layer of transcritical jets and variable-density jets can be considered to di¨er owing to pseudovaporization.

CONCLUDING REMARKS
The temperatures of transcritical and supercritical nitrogen jets were measured to explore the in §uence of pseudovaporization upon jet mixing.
Along the jet centerline, the decline in the temperature rise at the position where the local temperature reached near-pseudocritical temperature was caused by the large peak of isobaric speci¦c heat.Furthermore, the density jump appeared near the pseudocritical temperature; this can be correlated to the sudden expansion due to pseudovaporization.On the other hand, the axial pro¦les of the temperature and density of the supercritical jet monotonically increased and decreased, respectively, in the downstream region of the end of the jet potential core.
Similar to the axial pro¦les, the radial pro¦les of the temperature of the transcritical jet were in §uenced by pseudovaporization, i. e., the temperature rise in the radial direction became shallow in the region where the local temperature was lower than the pseudocritical temperature.The FWHM of the density pro¦les stayed almost constant further downstream of the end of the jet potential core, whereas of the mass fraction of the incompressible variable-density jet began to increase near the end of the potential core.Hence, the evolutions of the jet mixing layers of transcritical jets and incompressible variable-density jets can be considered to di¨er due to pseudovaporization.

Figure 2 Figure 3
Figure 2 Simpli¦ed diagram of experimental setup (TC ¡ thermocouple; P ¡ pressure sensor; and V ¡ valve): (a) §ow diagram and (b) LN2 pressurized reservoir and electric heater (dimensions are in millimeters)

Figure 6
Figure 6 Time-averaged backlit images of transcritical (a) and supercritical (b) jets

Figure 7
Figure 7 Temperature pro¦les of transcritical (a) and supercritical (b) jets and their axial gradient of temperature along the jet centerline (c): 1 ¡ transcritical jet; and 2 ¡ supercritical jet

Figure 8
Figure 8 Normalized density pro¦les of transcritical (a) and supercritical (b) jets and their axial gradient of density and mass fraction along the jet centerline (1 ¡ transcritical jet; and 2 ¡ supercritical jet) compared with the normalized mass fraction pro¦les of the incompressible variable-density jet (3) [7] (c)

Table 1
Injection conditions