Parametrical Study on Side Load Generation in Subscale Rocket Nozzles

The flow separation within convergent-divergent rocket engine nozzles induces undesired side loads. As the flow separation cannot be avoided during start-up and shut-down process of the engine the understanding of the resulting side loads is of crucial interest. To develop and validate side load models an experimental parameter study was conducted. The parameters of interest were the length of the separated backflow region, the wall contour angle and the total pressure gradient during start-up and shut-down process. For this reason three subscale models were designed and tested in five configurations. As the main side load driver a comparably slow moving separation front, passing a long and narrow backflow region, could be identified.


Introduction
The flow within a convergent-divergent rocket nozzle can only achieve a certain degree of overexpansion.Beyond, the boundary layer lifts off the nozzle wall and ambient air is sucked into the remaining separated backflow section of the nozzle.For a given nozzle geometry, the position of the flow separation is a function of the gas properties, the total and the ambient pressure.The prediction of the separation position is crucial for rocket engine design as it determines the maximum possible nozzle area ratio, a deciding factor for the engine performance.Nevertheless, during start-up and shut-down the total pressure of the engine changes, leading to flow separation within the divergent nozzle section.With increasing total pressure the flow separation is shifted downstream towards the nozzle exit until the engine operational condition with a full flowing nozzle is achieved.The flow separation is asymmetrically distributed in circumferential direction and the resulting wall pressure differences on opposite sides of the nozzle induce undesired side loads.These side loads, that cannot be avoided, stress the nozzle, the rocket engine, the engine actuators, the launcher structure and the payload.For this reason it is of interest to model and predict the side loads induced by flow separation.Successful side load prediction models will enable lighter nozzles, thrust chambers and actuators.Especially a reduced load transmission will profit the future application of lightweight electrical driven engine actuators.To generate side load model validation data DLR performed tests with three subscale nozzles under various conditions.The aim was to study the influence of parameters like length of separated backflow region or nozzle wall contour angle on side load generation.A special attention was put on the total pressure gradient, as this might be a deciding factor for modelling and comparison of nozzles of different sizes.

Experimental setup
The parametrical study was conducted at DLR's cold flow subscale test facility P6.2 in Lampoldshausen.Figure 1 gives a sketch of the facility assembly with its 20 MPa high pressure gaseous nitrogen supply storage.The line system includes automatic valves, filters, pressure reducers, regulation valves and mass flow meters.It connects the supply storage with the settling chambers, mounted vertically at the top of the high-altitude chamber (middle) or horizontally at the test rig (right).A third facility setup offers an additional ejector system to decouple the high altitude chamber pressure from the test specimen throughput (left).To reduce turbulence the settling chambers are equipped with a set of grids and honeycombs.The presented study was performed under ambient conditions using the horizontal test rig.

Nozzle design
For the purpose of this study three truncated ideal contour (TIC) nozzles have been designed.The nozzles feature design Mach numbers of Ma D = 4.8, 5.3 and 5.8.They are designated as TIC-2048, TIC-2053 and TIC-2058.The nozzles share the same subsonic geometry with a throat radius of R th = 10 mm.Each one of them was truncated to a length allowing full flowing condition at a nozzle pressure ratio of NPR = 50 (p 0 /p a ), leading to identical wall exit pressures with a wall exit Mach number of Ma e = 4.25.The specimens were made of acrylic glass with a wall thickness of 8 mm.The main nozzle design parameters are given in Table 1.

Pressure and side load measurement
The nozzles were equipped with two axial rows of pressure ports.One row featured a constant axial spacing of 4 mm.Depending on the nozzle configuration 16 to 30 ports could be implemented.The second row was radially shifted with 90° (see Fig. 3, left).Its port arrangement reproduces the wall Mach number progress.The resulting data are more suitable for a statistical validation of wall Mach number based separation criteria [1].
The static wall pressures were measured via 0.5 mm orifices, drilled perpendicular into the nozzle wall.These orifices were connected with small metal pipes and Teflon tubes to collecting blocks where piezo-resistive Kulite XT-154-190M absolute pressure transducers were screwed into.The transducers had a measurement range of 1 bar with an accuracy of 0.5%, relative to the upper range limit.The natural frequency of the transducers pressure sensitive semiconductor membrane is higher than 50 kHz but, due to the low eigenfrequency of the Teflon tubes, the pressure signals were filtered with a cut-off frequency of 160 Hz and recorded with a frequency rate of 1 kHz.Three selected port signals were recorded with a high frequency of 25 kHz.The setup was calibrated with different weights acting at the nozzle exit plane.The weights were applied with a string and releasing the weight by cutting its string (Fig. 3, right) gives the static as well as the dynamic response of the system.With this calibration all measured voltage signals can be interpreted as loads acting at the end of the nozzle.
Figure 5, left gives a calibration example where a force of 54 N is applied at the exit of nozzle TIC-2053.After release of the weight the vibration characteristic of the bending tube appears with a damped beat frequency.The dominant frequency is 390 Hz and the superposed frequency is 300 Hz.All bending data were recorded with a frequency of 25 kHz, using a signal filter of 8 kHz.

Test sequence
Figure 5, right depicts the NPR (p 0 /p a ) sequence used to test all five nozzle configurations.Three successive up-and down-ramping NPR gradients were realized: 25, 4.5 and 1.5 s -1 , respectively.In total 47 tests were performed (see Table 2).As all nozzles were tested with this common test sequence the resulting side load measurements can be compared easily.

Results and discussion
Three parameters were studied, the length of the separated backflow region, the wall contour angle and the NPR gradient.Figure 6 gives a representative side load measurement for the initial TIC-2048 nozzle.It appears that the side loads increase with decreasing NPR gradient.The side load data are standardised by the maximum side load peak occurred in Test 481, Run 8.All following side load charts are standardized by this value as well, so a direct comparison is given.
Figure 6: NPR and side load progress Figure 7 illustrates the same side loads as a function of the NPR gradients, both for up-ramping (left) and downramping process (right).The mean side load values appear to be lower for the down-ramping process, whereas the appearances of the peak values are comparable.Two distinct conditions with increased side loads are visible.The first one appears for a NPR below 10.Here, the boundary layer relaminarizes within the throat section due to the flow acceleration as a function of the local viscosity.In consequence, a laminar flow separation develops downstream the nozzle throat.With increasing NPR the flow separation is shifted downstream towards the nozzle exit.As the local Reynolds number increases along the nozzle wall, at a certain point a re-transition to a turbulent boundary layer takes place.The turbulent flow separation is known to withstand higher pressure differences, so the flow separation is immediately shifted downstream.As the re-transition process is circumferentially inhomogeneous distributed the resulting shock system of oblique separation shocks and Mach disc is tilted.The tilted Mach disc redirects the flow towards the wall where it reattaches partially.The resulting pressure differences on opposite side of the walls result in side loads [1,2].This stable flow state is called partial restricted flow separation, pRSS.gradient that accelerates the downstream movement of the separation position, damps the side load generation as the nozzle exit transit time is reduced.In reverse, for stationary or quasi stationary flow conditions (low NPR gradient), side loads might be intensified to an unrepresentative value that might not be useful for model validation or at least this flow state might have to be considered within modelling.

Length of separated back flow region
Figure 9 compares representative side loads of the successively truncated TIC-2048.The truncation positions can be found in Fig. 2, left and Table 1.It emerges that the truncation of the nozzle reduces the side loads.The impact of NPR gradient disappears and the peak value caused by pRSS decreases, as the lever arm of the reattached flow is reduced.The NPR of the peak's appearance does not change either.The relaminarization is a function of the throat geometry and the gas properties, parameters that do not change.The second side load maximum, caused by the fluctuating contact point, is shifted to lower NPRs.This is an expected result.The nozzle exit is relocated upstream and the contact point crosses it for lower NPR.The successively truncated nozzles show almost no impact of the NPR gradient.It implies that the intensification of the back flow disturbances at low NPR gradients does not appear.This might be caused by the separation related wall contour angle.An increased wall angle goes ahead with an increased wall Mach number gradient.Hence, the length of the separation zone with its fluctuating shock position is decreased in axial direction and the fluctuation of the linked contact point is reduced as well.The back flow disturbances are no longer intensified in a distinct quality.As mentioned, the flow separation fluctuates less in axial direction if the angle is steeper.As a consequence the closed loop of separation, exhaust jet and backflow is less activated.On the contrary, low wall angles narrow the back flow region and the feedback effect induced by the exhaust jet gains influence.It is noticeable that the trend detected for the truncated TIC-2048, where the maximum side load is shifted for each additional truncation towards a lower NPR, reverses and the maximum side loads are shifted to a higher NPR with increasing design Mach number.This effect is particular noticeable for the lowest NPR gradient.The ratios of NPR for the full flowing nozzle (see section 2.2) and related mean contact point transit NPR FF /NPR trans yield for all five configurations comparable values of 1.6 -1.8 (see Table 3).This correlation might ease the modelling and will be in focus for future studies.

Conclusions
Tests were conducted to study the impact of the separated backflow region length, the wall contour angle and the NPR gradient on side load generation.It appears that a slow moving separation front, passing a long and narrow backflow region, causes strongly increased side loads.As this slow movement is not the case for real rocket engine applications such quasi stationary validation configurations should be avoided or at least the slow NPR gradient should be included in modelling.Hence, as the main side load driver by design the nozzle exit wall angle can be identified.

a
Initial design / first truncation / second truncation One of the main factors of side load generation seems to be the inflow of ambient air into the separated back flow region.Hence, it was foreseen to truncate nozzle TIC-2048 twice to obtain nozzles being full flowing for a NPR of 40 and 30 (see Fig.2, left).With the resulting five configurations it was possible to study the impact of the length of the separated back flow region and the wall contour angle as well.

Figure 4 :
Figure 4: Sketch of bending tube (left) and strain gauges application (right)

Figure 7 :
Figure 7: Side loads as a function of NPR gradient

Figure 8 :
Figure 8: Side load maxima (left) and sketch of flow condition (right)

Figure 9 :
Figure 9: Side loads of initial TIC-2048 and after first and second truncation

Figure 10 presents a comparison
Figure10presents a comparison of TIC-2048, TIC-2053 and TIC-2058.The side loads decrease with increasing design Mach number.Likewise the effect of NPR gradient reduces.However, the overall side loads are still above the values of the truncated TIC-2048.As mentioned, the flow separation fluctuates less in axial direction if the angle is steeper.As a consequence the closed loop of separation, exhaust jet and backflow is less activated.On the contrary, low wall angles narrow the back flow region and the feedback effect induced by the exhaust jet gains influence.It is noticeable that the trend detected for the truncated TIC-2048, where the maximum side load is shifted for each additional truncation towards a lower NPR, reverses and the maximum side loads are shifted to a higher NPR with increasing design Mach number.This effect is particular noticeable for the lowest NPR gradient.The ratios of NPR for the full flowing nozzle (see section 2.2) and related mean contact point transit NPR FF /NPR trans yield for all five configurations comparable values of 1.6 -1.8 (see Table3).This correlation might ease the modelling and will be in focus for future studies.

Table 2 :
Performed number of tests

Table 3 :
Measured side loads