Conceptual Design Model of High-Altitude Test Stand for Rocket Engines *

Transcription

1 Trans. Japan Soc. Aero. Space Sci. Vol. 59, No. 3, pp , 2016 Conceptual Design Model of High-Altitude Test Stand for Rocket Engines * Takeshi KANDA, 1) Yohei OGAWA, 2) Daizo SUGIMORI, 3) and Makoto KOJIMA 1) 1) Research and Development Directorate, JAXA, Kakuda, Miyagi , Japan 2) Research and Development Directorate, JAXA, Tsukuba, Ibaraki , Japan 3) Space Technology Directorate I, JAXA, Tsukuba, Ibaraki , Japan Conceptual design procedures and design models of HATS are revised and renewed. The results calculated using the revised method are compared with the operating conditions of HATS at the JAXA Kakuda Space Center. The previous physical method of test chamber pressure and that of ejector suction are adopted in the present model. The suction model adopts the inviscid momentum exchange mechanism. The deceleration process in the supersonic diffuser is revised using the pseudo-shock model. Physical and thermodynamic models are constructed for condensation and steam saturated flow conditions. The results calculated are in reasonable agreement with the measured values (e.g., pressure of secondary flow at the ejector section and pressure changes during engine shut down). The effect of ejector steam condensation on the operating conditions of HATS is quantitatively presented. Key Words: HATS, Rocket Engine, Ejector, Diffuser, Condensation, Saturation Nomenclature A F: coefficients of vapor pressure equation A: cross-section F: impulse function, force f: streamwise component of force h v : latent heat h: enthalpy L: length M: Mach number _m: mass flow rate p c : critical pressure p v : vapor pressure p: mean pressure s: entropy T: temperature T c : critical temperature T r : normalized temperature by T c u: velocity x: dryness, parameter of temperature Subscripts a: test chamber e: outflow f: friction g: saturated vapor, gas i: entrance of HATS diffuser, inflow l: saturated liquid, liquid p: pseudo-shock r: reaction ref: nominal condition rk: rocket t: total 2016 The Japan Society for Aeronautical and Space Sciences + Received 16 July 2015; final revision received 5 November 2015; accepted for publication 18 January Corresponding author, kanda.takeshi@jaxa.jp x: mixture 1: condition 1, fluid 1, upstream of pseudo-shock 2: condition 2, fluid 2, downstream of pseudo-shock 1. Introduction The High-Altitude Test Stand (HATS) is a facility for testing upper-stage rocket engines. HATS creates a high-altitude environment, and the rocket engines operate under low-pressure conditions created by HATS. JAXA has two HATS facilities at the Kakuda Space Center. 1) One was constructed by National Aerospace Development Agency (NASDA) and is used for development tests and acceptance tests of upper-stage engines. It is called NASDA-HATS in the present study. The other was constructed by the National Aerospace Laboratory (NAL) as the pilot HATS for NAS- DA-HATS and is primarily used for research activities. It is called NAL-HATS. These facilities were designed and constructed about 40 years ago. There are several HATS facilities in the world (e.g., facilities at Stennis Space Center, 2) White Sands Test Facility, 3) Plum Brook, 4) and Lampoldshausen 5) ). In the construction of a new facility, a conceptual study is first conducted to specify requirements. The study progresses by examining exiting physical models, design tools and design data, and shows an outline of the facility. Based on the results of the conceptual study, details of the facility are designed, development tests and simulations are conducted, and the facility is constructed. In the construction of Japan s HATS, the same process was conducted. There are reports of the conceptual study on the JAXA HATSs in the form of a technical report or a technical memorandum of the National Aerospace Laboratory, Japan. The other HATS reports present facility specifications or component study results, not facility conceptual study results. In the conceptual design process of the two JAXA HATSs, several physical models and estimation formulas were used 161

2 Fig. 1. Schematic of a HATS. and the estimated results were verified experimentally. 6,7) In the design process, some parameters were specified experimentally. In the present study, the conceptual design models and design procedures of the HATSs are reviewed and revised. Over the 40 years, several technologies have been constructed, and there are findings on physical mechanisms relating to HATS operation. Some are applied to the present conceptual design model of HATS. The results calculated by the present procedure can be an initial configuration in the HATS design process and in CFD simulation. The present physical models and the procedures will be applied to design other systems (e.g., an exhaust system of wind tunnels, ejector pumps, and saturation of working gases) in which similar or the same physical phenomenon are utilized as in the HATSs. 2. HATS Operation Both the NASDA-HATS and the NAL-HATS are comprised of two steam ejectors and three diffusers. The ejectors are located in the center of the duct. Herein, the operation of a HATS is explained with this configuration. Figure 1 shows a schematic of a HATS. A HATS creates a low-pressure condition in the test chamber through ejector operation. The exhaust-gas pressure is recovered in the diffuser. The combustion gas of a rocket engine expands from the exit of the nozzle. The flow-field of the re-attachment of the combustion gas specifies the pressure in the test chamber. The supersonic rocket engine combustion gas attaching to the HATS wall decelerates in the first diffuser and becomes subsonic, passing through the shock-train, or the pseudoshock. Cooling water is injected to the subsonic combustion gas. The mixture of the combustion gas and the steam of the cooling water is suctioned by the first ejector. Suction is necessary because the pressure of the rocket gas mixture is lower than the ambient pressure. At the same time, the total pressure of the rocket gas mixture is increased by mixing with the high-pressure ejector steam. Pressure is recovered in the second diffuser. The same suction and pressure recovery are conducted in the second ejector and third diffuser. The gas mixture is exhausted to ambient pressure. To match the exit pressure condition, the position of the pseudo-shock changes in the first diffuser. The major phenomena in a HATS are reattachment of the rocket gas to the wall, deceleration of supersonic gas flow, Fig. 2. Schematic of attaching supersonic flow behind the step. suction by the ejector, pressure recovery in the diffuser, and condensation of steam in the ejectors. 3. Physical Models for Calculation 3.1. Test chamber pressure The pressure of the test chamber is the most important specification in the high-altitude tests at a HATS. A two-dimensional, supersonic base flow model 8 10) was applied to attachment of the rocket combustion gas to the HATS duct wall during the design procedure of the two HATSs. Figure 2 shows a schematic of the flow-field. A supersonic fluid flows at the rearward facing step. The fluid expands isentropically at the corner of the step. The accelerated fluid attaches to the wall nonisentropically and creates a shock wave. The primary flow in Fig. 2 corresponds to the rocket combustion gas in the HATS, and the lower wall corresponds to the diffuser duct wall. The vertical wall in Fig. 2 corresponds to the opening between the rocket nozzle and the diffuser duct wall. In designing the HATSs, the pressure of the test chamber was estimated by the pressure in the base region behind the step. The present study also adopts the base flow model to estimate the pressure of the test chamber. There are several flow models and equations for the base pressure. In the present study, the empirical pressure equation is adopted. 9) A one-dimensional flow model can be applied to this process for attaching the rocket combustion gas to the HATS duct wall. Expansion of the rocket exhaust to the HATS duct wall was calculated assuming isentropic change. The rocket combustion gas receives reaction force from the pressure of the test chamber during the expansion process. This pressure is 162

3 Fig. 3. Schematic of pseudo-shock. not equal to the pressure in the isentropic change. In the present study, the one-dimensional flow model is also used for attachment with nonisentropic change. The impulse function of the expanded, attached rocket exhaust is F ¼ F rk þða i A rk Þp a ð1þ 3.2. Pseudo-shock in diffuser The supersonic, rocket engine combustion gas decelerates to subsonic flow through the shock train, or the pseudoshock, in the first diffuser. This phenomenon affects pressure recovery performance in the diffuser. The starting position, or length of the pseudo-shock, affects the required length of the duct. Studies on the pseudo-shock has been conducted. 11) Recently, the starting position of the pseudo-shock was estimated using the momentum balance model. 12) In the model revised for the present study, this estimation method is newly adopted to calculate the position of the pseudo-shock and pressure recovery performance of the first diffuser. This model can be applied to a diffuser of supersonic/hypersonic wind tunnels. The impulse function of the supersonic inflow is not generally equal to that of the subsonic outflow. The boundary condition (e.g., pressure or choking) is applied to the subsonic outflow. On the other hand, there is little friction force in the pseudo-shock region because the boundary layer thickens and separation may appear in the region. Figure 3 shows a schematic of the flow-field with the pseudo-shock. Force balance is written as F e ¼ F i þ f r1 þ f rp þ f r2 f f1 f f2 ð2þ where f r2 is the streamwise component of reaction force, which appears when the end of the pseudo-shock is upstream of the divergent section exit. In the momentum balance model, there is no friction in the pseudo-shock region. By balancing the inflow and outflow impulse functions, the starting position of the pseudo-shock is specified. The length of the pseudo-shock is several times the diameter of the duct. 13) Herein, the length is assumed to be five times larger. Studies on the length of the pseudo-shock are under investigation. When the presumed length of the pseudo-shock is too large, the pseudo-shock starts from the entrance of the first diffuser, especially under the throttled condition of a rocket engine. This pseudo-shock condition interacts with the attachment of rocket engine exhaust to the HATS duct wall, and induces the diffuser break. In the actual operation of a HATS, the diffuser break is measured prior to arrival of the pseudo-shock to the diffuser entrance. As presented later, the results calculated are close to the operating conditions of the HATS. The presumed ratio of the pseudo-shock length would be close to the actual length. When the position of the pseudo-shock is located relatively downstream in the first diffuser, the end position of the shock wave is in the mid of the divergent section in the diffuser. Downstream of the pseudo-shock, pressure is recovered approximately in the isentropic change. As the pseudoshock moves upstream, the Mach number becomes smaller, the shock wave becomes weaker, and total pressure loss becomes smaller. With the momentum balance model, the performance of pressure recovery can be estimated. Since the position of the pseudo-shock changes due to the operating conditions of the rocket engine tested, the required length of the diffuser duct can be confirmed with the model. When the rocket engine decreases its thrust during shutdown, the momentum in the HATS duct decreases and the pseudo-shock is moved toward the entrance of the HATS duct. As the pseudo-shock exists upstream, the momentum and pressure recovery of the HATS are improved. After the shock wave arrives at the entrance, pressure in the test chamber increases, and the rocket combustion gas detaches from the HATS duct wall. The diffuser operates as a subsonic diffuser. This increase in pressure and the change in flow condition is called the diffuser break. The one-dimensional model is used after the diffuser break. In simulating the diffuser break using the one-dimensional model, the rocket gas expands to the pressure of the test chamber, p a, and the gas flow detaches from the HATS duct wall. In the second and third diffusers, the secondary subsonic flow rate is large, and the pseudo-shock model is not applied to the diffusers. The primary, supersonic flow of the ejector steam and the secondary, subsonic flow mix together. The subsonic mixed gas recovers pressure in the divergent section of the diffuser, which is calculated under the assumption of isentropic change. Cooling of the supersonic diffuser has been studied. 14,15) Supersonic combustion gas flow decelerates to subsonic through the pseudo-shock. The general estimation formula for heat transfer is not effective in the pseudo-shock region. Cuffel and Back showed a ratio of heat fluxes was proportional to 0.8 power of a ratio of wall pressures for air in a straight duct. 14) Recently, Kato and Kanda extended the model of Cuffel and Back to a divergent duct and a combustion gas. 16) 3.3. Vaporization of water and condensation of steam Water is sprayed to the combustion gas of the rocket engine for cooling and vaporizes around the exit of the first dif- 163

4 Mach number at exit of nozzle Trans. Japan Soc. Aero. Space Sci., Vol. 59, No. 3, 2016 Table 1. Total pressure, MPa Pressure at the exit of hypersonic wind tunnel. Design pressure (no condensation), kpa Calculated pressure by saturated N2, kpa Measured pressure, kpa fuser. The gas after water-cooling is a mixture of the combustion gas and cooling water. The steam is in a saturated condition and its properties are different from those of a pure gas. The dryness of the saturated steam and flow conditions of the steam are calculated to estimate ejector performance. Mean specific heat is calculated with mean molecular weight. No cooling water momentum, liquid water volume, or effect of liquid water on the sound speed of the gas are presumed. Liquid water has no relation to the ideal gas equation. The velocity of the liquid is the same as that of the gas here. Momentum is conserved prior to and after condensation. Enthalpy is calculated with latent heat. The energy conservation is expressed as Here _m h t ¼ _m g h t;g þ _m l h t;l h t;l ¼ h t;g h v ð4þ Dryness, x, is a ratio of the gaseous mass flow rate to the total flow rate. x ¼ _m g = _m The latent heat of water is calculated using the formula of Watson. 17) Here h v;2 ¼ h v;1 fð1 T r;2 Þ=ð1 T r;1 Þg 0:375 T r ¼ðT=T c Þ The saturated vapor pressure of steam is calculated using the formula of Wagner and Pruss.! 18) ln p v ¼ T c T ðaxþbx1:5 þ C x 3 þ D x 3:5 Here p c þ E x 4 þ F x 7:5 Þ x ¼ 1 ðt=t c Þ A ¼ 7: ; B ¼ 1: ; C ¼ 11: ; D ¼ 22: ; E ¼ 15: ; F ¼ 1: Condensation of steam happens in the ejector nozzles. Its effect was simulated by changing the ratio of specific heats in the design process of the HATSs. 19) In the present study, the dryness and properties in the ejector nozzles are calculated assuming isentropic change. This process is similar to that of the equilibrium flow of combustion gas in rocket nozzles. There are recombination ð3þ ð5þ ð6þ ð7þ ð8þ ð9þ of molecules, change of mean molecular weight and release of heat under the assumption of isentropic change. It is well known that the equilibrium flow calculation of rocket combustion gas reasonably predicts the performance of the rocket nozzles. In the ejector nozzles, the molecular weight of the gas changes due to condensation and latent heat is released. A similar change as in the rocket nozzles progresses in the ejector nozzles. Entropy is calculated using the general thermodynamic relation below. 20) s ¼ s g þfð1 xþh v g=t ð10þ This isentropic flow model with condensation is verified using the results of hypersonic wind tunnel nozzle flows. 21) The Mach numbers of the nozzles are 5.4 and 6.7, respectively. The fluid of the experiments was air at room temperature, whereas the calculation is conducted using the properties of nitrogen. Table 1 lists the test condition and the pressures measured and calculated. The design pressure was calculated using the ideal gas relation with no condensation. The pressure calculated with condensation was higher than the design values and close to the measured values, respectively. One of the reasons for the difference is deviation of the flow conditions in the wind tunnel nozzles from the designed flow conditions due to condensation. According to the present calculation with condensation, the pressure measured corresponds to the Mach 4.7 flow condition, whereas the Mach number calculated is 4.8 for the Mach 6.7 design condition. For the Mach 5.4 condition, both measured and calculated Mach numbers correspond to the Mach 4.5 condition Ejector system The primary, supersonic steam of the ejector interacts with the secondary, subsonic fluid, which is a mixture of the rocket combustion gas and cooling water. In the second ejector system, the secondary mixed flow also contains steam from the first ejector. By the interaction, the secondary fluid is pumped out or suctioned. Figure 4 shows a schematic of the ejector system flow-field. Momentum is exchanged in the interaction of the two flows in an almost inviscid process. This inviscid, momentum exchange mechanism has been presented (e.g., by Fabri and Siestrunck) and verified experimentally. 22) This model was adopted in the HATS design process. The present model also adopts this mechanism. This inviscid model is a general basis for most ejector systems. The conservations of mass, momentum and energy, relation between pressures and relation between cross-sections are _m 0 1 ¼ _m 1 ð11þ _m 0 2 ¼ _m 2 ð12þ 164

5 (a) Fig. 5. Entropy changes due to momentum exchange along the mean pressure, p. _m 0 1 u0 1 þ A0 1 p0 1 ¼ _m 1 u 1 þ A 1 p 1 A p _m 0 2 u0 2 þ A0 2 p0 2 ¼ _m 2 u 2 þ A 2 p 2 þ A ~p p 0 2 ¼ p0 1 A ¼ A 0 1 A 1 ¼ A 2 A 0 2 h 0 t;1 ¼ h t;1 h 0 t;2 ¼ h t;2 (b) Fig. 4. Schematic of the ejector. Secondary flow is subsonic. In (a), pressure of the secondary flow is higher than that of the ejector gas flow. In (b), pressure of the secondary flow is lower than that of the ejector gas flow. ð13þ ð14þ ð15þ ð16þ ð17þ ð18þ The condition after the momentum exchange is expressed with a prime. p 1 is not usually equal to p 2, whereas pressure is equal both in the primary and secondary flows after the momentum exchange. p is the mean pressure during the exchange. A p can be negative. Momentum is exchanged at the dividing streamline. Some of the previous studies calculated changes in flow condition using the method of characteristics. In the present model, the exchange is calculated in a simplified way. 23) Pressure after the interaction, p 0 2 or p0 1, is used for the mean pressure on the dividing streamline, p. Simplification of the pressure was verified by comparison with the experimental results. 24) There are several kinds of inflow boundary conditions for the primary and secondary fluids. For example, the pressure of the supersonic primary flow is presumed to be lower than that of the subsonic secondary flow. The primary flow increases pressure through shock waves and is still supersonic after the interaction. The pressure of the secondary flow decreases even though the flow diverges. It is generally a contradiction to the pressure-cross-section relation. This can happen in the non-isentropic change. As Fabri mentioned, momentum exchange is not an isentropic process. 22) In the present study, this combination of primary and secondary flows is calculated with in a simplified way. In the previous study, this flow condition was not discussed. Figure 5 shows an example calculation result for the relationship between the mean pressure, p, and increases in entropy. Fluid 1 is supersonic steam and fluid 2 is subsonic steam. The total temperature is 400 K and the mass flow rate is 50 kg0s ¹1 for both fluids. The total pressure of fluid 1 is 500 kpa and that of fluid 2 is 40 kpa. The cross-section of fluid 1 is 0.4 m 2 and that of fluid 2 is 2 m 2. In this example calculation, the interacting pressure is equal to the pressure after the interaction, as in the present simplified calculation. Mean entropy after the interaction is calculated with each entropy by weighing each mass flow rate. Mass, momentum and energy are conserved at the mean pressure of 38.4 kpa, indicated as Interacting pressure in the figure. The pressure is slightly lower than the pressure of fluid 2, 38.5 kpa, prior to the interaction. The entropy increases slightly in fluid 2 at the mean pressure, whereas the increase in fluid 1 is extensive. The change of the cross-section is 0.19 m 2 under these conditions. With these conditions, the ejector works to hold a lowpressure environment for the secondary flow and to increase the total pressure of the secondary flow by mixing the primary flow downstream of the momentum exchange. When pressure in the secondary flow is lower than that in the primary flow at the entrance of the ejector section, the primary flow expands and the secondary flow converges. The pressure for both is lower than that of the flows prior to the momentum exchange. Figure 4(b) shows a schematic of these conditions. The secondary flow may choke. This is called Fabri choking and appears when starting and shutting down a rocket engine. It was found that mixing degrades the suction performance of the ejector. 25) Attention is required when designing the ejector Calculation procedure With these physical models and assumptions, flow in HATS is calculated. New physical modes are used for the pseudo-shock in the first diffuser and steam properties in 165

6 the ejector nozzles, and pressure of the test chamber in the 1- D model. The same models as those in the previous study are used for suction performance of the ejectors and pressure of the test chamber with the base-flow model. For the estimation of pressure in the test chamber, a new 1-D model and a conventional model are used. The exit boundary condition is a specified pressure of 1.05 atm, being larger than 1 atm due to the loss of pressure in the silencer downstream of the third diffuser. The upstream boundary condition is the inflow of the rocket combustion gas. The pseudo-shock position is located to balance the inflows and outflows of mass, momentum and energy. The ratio of the specific heat is 1.33 for steam. The properties of steam are calculated under the assumption of invariable specific heat. It is assumed there is no friction in the pseudo-shock region, 12) whereas the friction coefficient is set to be ) Heat transfer is calculated using the Reynolds analogy. Wall temperature is set to 350 K. 4. Results and Discussion Application of the physical models is verified by comparing the calculated and measured operating conditions of the NAL-HATS. 27) The specifications of the NAL-HATS are listed in Table 2. The specifications of the engine tested are listed in Table 3. Though the test results of another engine are also described in the report, most of the HATS operating tests were conducted with the engine listed in Table 3. In the present study, another calculation is conducted under the condition that the outer diameter of the secondary flow duct exit of the second ejector section is reduced to 90%, besides the calculation using the original geometry. Under the original geometry, when the rocket engine thrust is reduced, the pseudo-shock is located at the entrance of the first diffuser and the exit pressure of the HATS is calculated to be lower than the specified exit pressure. By reducing the diameter, the position of the pseudo-shock is still in the mid of the first diffuser even under the reduced-thrust condition. This effect is also attained by reducing the outer diameter of the secondary flow of the first ejector section. Details are described in Section 4.2. This reduction of the cross-section may represent the effect of displacement thickness of the boundary layer. The NAL-HATS was operated by injecting a small amount of air under no rocket exhaust condition for steady operation of the ejector. At the renewal of the NAL-HATS in 2011, the outer diameter of the secondary flow duct of the first ejector section was reduced. The effect of reducing the diameter is shown in Fig. 6. In this example calculation, the mass flow rate and total temperature of the secondary flow are set to be 50 kg0s ¹1 and 500 K, respectively. Those of the primary flow are 122 kg0s ¹1 and 500 K, respectively. The total pressure of the primary flow is 1.30 MPa and the Mach number at the exit of the ejector nozzle is 1.5 or 2.5. The static pressure of the secondary flow is the same as that of the primary flow at the nozzle exit. These are similar to the operating conditions of the NAL- HATS. The static pressure of the secondary flow is equal to that of the primary flow for simplicity. Then, the velocity of the secondary flow is specified by the pressure condition. The cross-section of the secondary flow is a parameter. As the cross-section is decreased, the total pressure of the mixture is increased. The Mach number of the secondary flow becomes large as the cross-section decreases, and the flow chokes at A 2 =A 1 ¼ 1:33 in the case of M 1 ¼ 2:5. As the cross-section of the secondary flow decreases, the velocity of the secondary flow becomes close to that of the primary flow. This reduces the increase in entropy during mixing. In the design process, selection of the secondary flow cross-section of the ejector section is an important parameter. In this section, the results with the 90% outer exit diameter are referred to, as well as those with the original configuration. Table 3. Specifications of the rocket engine tested. Propellants NTO/A-50 Thrust, kn 53 Chamber pressure, MPa 1.2 Area ratio of nozzle 26 Propellant flow rate, kg0s ¹ Diameter at throat, mm 185 Diameter at exit, mm 944 Table 2. Specifications of the NAL-HATS. Diameter, length and exit diameter of 1st 1:1 12 2:0 diffuser, m Sprayed cooling water, kg0s ¹1 35 (50 kn eng.) Mass flow rates of steam ejectors, kg0s ¹1 40 (1st ejector) 120 (2nd ejector) Area ratio of ejector nozzles 11.6 (1st ejector) 5.5 (2nd ejector) Diameter, length and exit diameter of 2nd 1:4 20 2:6 diffuser, m Diameter, length and exit diameter of 3rd 1:4 21 2:4 diffuser, m Fig. 6. Relation between secondary flow cross-section and total pressure of the ejector system mixture. 166

7 Fig. 7. Pressure of secondary flow of the 2nd ejector section. Fig. 8. Changes of pressure and thrust during engine shut-down. 27) In the accumulator, the temperature was higher than the saturated temperature. However, the duct from the accumulator to the ejector has length, and the dryness at the exit of the accumulator was lower than unity. 27) In the present study, the total temperature of steam is the saturated temperature at the stagnation pressure in the ejector manifolds as a reference condition. Calculation with the superheated steam can be conducted using the present model and the results are referred to later Operation of second ejector Figure 7 shows pressure of the secondary flow at the entrance of the second ejector section along the steam stagnation pressure of the second ejector. The calculated pressures are plotted in the figure. In the calculation, the mass flow rate of the cooling water sprayed is 35 kg0s ¹1. The mass flow rate of the secondary flow is 94 kg0s ¹1 and the calculated flow rate is 93 kg0s ¹1. The total temperature of the secondary flow is 445 K. The calculated pressures of the secondary flow reasonably agree with the values measured within the convergence error of the calculation. In the previous design process, the calculated pressure of 60 kpa was attained with the flow rate of 140 kg0s ¹1, which was about 1.5 times larger than the actual flow rate. 27) The pressure of 40 kpa was attained with secondary flow rate of 85 kg0s ¹1, which was 0.9 times the actual flow rate. Qualitative agreement between the calculated and experimental results was addressed. The large difference in the previous calculation would be due to the difference in application of the ejector model, described in Section 3.4. The accuracy is improved in the present HATS design model Test chamber pressure and diffuser break Figure 8 shows changes in the test chamber pressure, wall pressure of the first diffuser and normalized thrust in the engine shut-down process when testing the NAL-HATS. Time measurement started from engine ignition. At 20.81s, the thrust ratio was about 0.6 and the diffuser break happened. Pressure in the test chamber increased after the break. Under the break condition, the rocket engine combustion gas might detach from the HATS duct. The test chamber pressure measured was 1.1 kpa under the design operating conditions. The calculated pressure was 0.4 kpa using the base flow equation and is 1.6 kpa using the one-dimensional, nonisentropic expansion model. There would be measurement and convergence errors. The transient operating condition of the HATS would be different from that in the calculation. This conceptual study calculates steady-state conditions. Under such conditions, the calculations predict approximate pressure. There was no comparison of this pressure history between the measured and the calculated results in the previous study. 27) The diffuser break condition is studied using the one-dimensional model. Until the diffuser break, the rocket exhaust expands nonisentropically to the duct wall and the impulse function of the attached combustion gas flow is calculated using Eq. (1). In the diffuser break condition, the rocket exhaust expands to the test chamber pressure and detaches from the HATS duct wall. The impulse function is the sum of the rocket exhaust momentum and the force of the chamber pressure. The change from attachment to detachment is caused by the momentum balance to attain the HATS exit pressure condition. The diffuser break, which is detachment of the rocket exhaust from the wall, is calculated to happen at the thrust ratio, F=F ref, of 0.55 when the outer diameter is reduced to 85%. In the experiment, the break, which was defined by an abrupt change in pressure, happened around the thrust ratio of 0.6, as shown in Fig. 8. The diffuser break calculated with the present model agreed reasonably well with the experimental break. In the present calculation, the test chamber pressure is 0.9 kpa prior to the diffuser break, whereas it is 4.7 kpa at the thrust ratio of 0.45 after the break. In the experiment, it was 1.1 kpa prior to the break, and 4.7 kpa at the ratio of These pressures agree reasonably with the values measured. There was no comparison on this pressure history between the measured and the calculated results in the previous study. 27) 167

8 4.3. Condensation of steam in ejector nozzle The comparisons in the previous sections show the present model predicts the operating conditions of a HATS reasonably well. In the comparisons, the effect of condensation is already included. In this section, the effect of steam condensation is discussed. In the present study of HATS operation, calculation of steam condensation is conducted in all ducts and sections. As a result, condensation happens only in the ejectors. The discussion is limited to the flow in the ejectors. Condensation in the ejectors was well recognized in previous studies, however, a suitable model for saturated steam flow was not constructed. As described in Section 3.3, the effect of condensation was simulated by changing the ratio of specific heats. Dryness changes due to the local temperature and pressure conditions in the saturated flow, and uncertainty remains in the steam ejector performance. In the present study, the saturated steam flow is calculated using dryness and isentropic flow modeling. Part of the saturated steam condenses during expansion in the ejector nozzle. Steam is assumed to be in a saturated condition at 465 K at the pressure of the ejector manifold. The conditions for ejector steam and operating conditions are listed in Tables 4 and 5. Flow conditions in the superheated condition of 528 K are also listed in the tables. The temperature at the superheated condition is the saturated temperature of steam in the accumulator. For comparison, flow conditions of no gas condensation, in other words, no-liquid condition, are also listed. Total pressures of the mixture downstream of the second ejector (i.e., in the third diffuser) for the no-liquid cases are lower than the exit condition and are shown in parentheses. Results with the outer diameter reduced are listed on the right-hand side in the column. Condensation can even happen at the throat of the ejectors. This makes a difference in the design mass flow rate of the ejectors. At the exit of the ejector nozzles, condensation further progresses and total pressure becomes much lower than the pressure in the no-liquid cases. However, the impulse functions at the exit are approximately the same as those with no condensation in the previous ejectors. A small increase in the impulse function under the saturated condition is similar to increasing the thrust under the equilibrium flow condition. Differences appear in static pressure at the exit of the ejector nozzles, as well as the difference shown in Table 1. In the no-liquid cases, the pressure at the ejector exit is lower than that of the saturated condition. The difference between the pressure of the secondary flow and that at the ejector exit becomes great in no-liquid cases. The pressure in the third diffuser is specified by the pressure exit condition. When the loss of total pressure during mixing is small in the second ejector, high total pressure in the secondary flow is not required. Under the low total pressure condition of the secondary flow in the second diffuser, the pseudo-shock can be positioned in the mid of the first diffuser (i.e., at relatively downstream in the first diffuser). The small total pressure downstream of the first ejector is caused by this mechanism in the saturated steam cases. The effects of condensation in the ejectors should be included in the design procedure for HATS. Table 4. Calculated operating conditions of 1st ejector. 1st ejector Saturated Superheated No liquid (T t ¼ 465 K) No liquid (T t ¼ 528 K) Stagnation pressure, MPa Stagnation temperature, K Mass flow rate, kg0s ¹ Dryness at throat Dryness at exit of nozzle Pressure at nozzle exit, kpa Total pressure ratio at nozzle exit Impulse function, kn Total pressure of secondary flow, kpa 48.7/ / / /44.9 Total pressure of mixed flow, kpa 65.1/ / / /60 Pressure after suction of secondary flow, kpa 47.7/ Table 5. Calculated operating conditions of 2nd ejector. 2nd ejector Saturated Superheated No liquid (T t ¼ 465 K) No liquid (T t ¼ 528 K) Stagnation pressure, MPa Stagnation temperature, K Mass flow rate, kg0s ¹ Dryness at throat Dryness at exit of nozzle Pressure at nozzle exit, kpa Total pressure ratio at nozzle exit Impulse function, kn Total pressure of secondary flow, kpa 65.1/ / / /60 Total pressure of mixed flow, kpa 107/ /109 (105)/109 (105)/109 Pressure after suction of secondary flow, kpa 62.6/

9 5. Conclusion Conceptual design procedures and design models for HATS facilities are reviewed and revised. The results calculated using the present model were compared with the operating conditions of a previous HATS, and the present model was verified. The previous prediction method for the test chamber pressure is also adopted in the present model. The deceleration process was revised using the momentum balance model of pseudo-shock. The inviscid momentum exchange model of the ejector system that calculates operating conditions agreed with the conditions measured. The present model shows that condensation in the ejectors affects the HATS operating conditions. Acknowledgments The authors thank Mr. Kouichiro Tani and Mr. Takeo Tomita of JAXA for useful discussions and advices. References 1) JAXA Kakuda Space Center, index.html (accessed June 16, 2015) 2) Maynard, B. T. and Raines, N.: Altitude Testing of Large Liquid Propellant Engines, AIAA Paper , Seattle, Washington, USA, June ) Harris, D. and Cort, R.: White Sands Test Facility Test Stand 401, AIAA Paper , Cleveland, OH, USA, ) Kenzakowski, D. C. and Brinckman, K. W.: CFD Simulation of NASA B-2 Spray Chamber during Rocket Fire, AIAA Paper , Reno, NV, Jan ) Schäfer, K. and Zimmermann, H.: Simulation of Flight Condition during Lift OFF for Rocket Engine Testing, AIAA Paper , Fort Lauderdale, FL, USA, July ) Kumagai, T., Miyajima, H., Kamata, M., Satoh, M., Abe, N., Sudoh, T., Yamada, A., and Kouchiyama, J.: Simulation Test of Exhaust System of High Altitude Test Stand for LOX/LH 2 Rocket Engine, NAL TM-461, Mar (in Japanese). 7) Miyajima, H., Abe, N., and Kisara, K.: Design Calculation of Diffuser for Rocket Engine High Altitude Test Stand, NAL TM-313, Sep (in Japanese). 8) Korst, H. H.: A Theory for Base Pressure in Transonic and Supersonic Flow, J. Appl. Mech., 23, 4 (1956), pp ) Lamb, J. P. and Oberkampf, W. L.: Review and Development of Base Pressure and Base Heating Correlations in Supersonic Flow, J. Spacecraft Rockets, 32, 1 (1995), pp ) Karashima, K. and Hasegawa, K.: An Approximate Approach to Base Flow behind Two-Dimensional Rearward-Facing Steps Placed in a Uniform Supersonic Stream, ISAS Report, No. 501, 1973, pp ) Matsuo, K., Miyazato, Y., and Kim, H.-D.: Shock Train and Pseudo- Shock Phenomena in Internal Gas Flow, Progress in Aerospace Sciences, 35, 1 (1999), pp ) Kanda, T. and Tani, K.: Momentum Balance Model of Flow Field with Pseudo-Shock, JAXA Report, JAXA-RR E, Mar ) Kanda, T.: Prediction of Pseudo-Shock Position in a Long Duct Using the Momentum Balance Model, Trans. Jpn. Soc. Aeronaut. Space Sci., 55, 3 (2012), pp ) Cuffel, R. F. and Back, L. H.: Flow and Heat Transfer Measurement in a Pseudo-Shock Region with Surface Cooling, AIAA J., 14, 12 (1976), pp ) Zaikovskii, V. N., Trofimov, V. M., and Shtrekalkin, S. I.: Experimental and Computational Investigation of Heat Fluxes in a Supersonic Diffuser, J. Appl. Mechanics Rechnical Physics, 37, 1 (1996), pp ) Kato, K. and Kanda, T.: Calculation of Heat Flux in the Pseudo-Shock Region, 30th ISTS, 2015-a-59, Kobe, Hyogo, Japan, July ) Reid, R. C., Prausnitz, J. M., and Sherwood, T. K.: The Properties of Gases and Liquids, 3rd Ed., McGraw-Hill, New York, 1977, pp ) Wagner, W. and Pruss, A.: International Equations for the Saturation Properties of Ordinary Water Substance. Revised According to the International Temperature Scale of 1990, J. Phys. Chem. Reference Data, 22, 3 (1993), pp ) Miyajima, H., Yamada, A., Kisara, K., Kamata, M., Satoh, M., Ueno, T., Kumagai, T., and Kusaka, K.: Experiments on Steam Ejectors for Rocket Engine Altitude Simulation, NAL TR-566, Apr (in Japanese). 20) Iinuma, K.: Engineering Thermodynamics, 4th Ed., Gakutoh Co. Ltd., Tokyo, 1979, pp (in Japanese). 21) Mitani, T., Hiraiwa, T., Kanda, T., Shimua, T., Tomioka, S., Kobayashi, K., Izumikawa, M., Sakuranaka, N., Watanabe, S., Tarukawa, Y., Kouchi, T., Kitamura, E., and Yatsunami, T.: Subscale Wind Tunnels and Supplemental Studies of Scramjet Engine Tests, NAL TR-1458, Apr (in Japanese). 22) Fabri, J. and Paulon, J.: Theory and Experiments on Supersonic Air-to- Air Ejectors, NACA TM 1410, Jan ) Kanda, T. and Kudo, K.: Conceptual Study of a Combined-Cycle Engine for an Aerospace Plane, J. Propul. Power, 19, 5 (2003), pp ) Aoki, S., Lee, J., Masuya, G., Kanda, T., and Kudo, K.: Aerodynamic Experiments on an Ejector-Jet, J. Propul. Power, 21, 3 (2005), pp ) Tani, K., Hasegawa, S., Ueda, S., Kanda, T., and Nagata, H.: Analytical Method for Prediction of Suction Preformance of Ejector-Jet, Trans. Jpn. Soc. Aeronaut. Space Sci., 58, 4 (2015), pp ) White, F. M.: Viscous Fluid Flow, McGraw-Hill, New York, 1974, pp. 495, ) Ohtsuka, S., et al.: High Altitude Test Facility for Rocket Engine at NAL, National Aerospace Laboratory, NAL TR-454, Apr (in Japanese). T. Shimada Associate Editor 169