Shock Waves (2009) 19:185–191 DOI 10.1007/s00193-008-0174-6
ORIGINAL ARTICLE
Experimental study of boundary layer separation in truncated ideal contour nozzles Ralf Stark · Bernd Wagner
Received: 8 May 2008 / Revised: 20 August 2008 / Accepted: 14 October 2008 / Published online: 7 November 2008 © Springer-Verlag 2008
Abstract DLR Lampoldshausen carried out a cold flow test series to study the boundary layer separation and the related flow field in a truncated ideal contour nozzle. A special focus was set on low nozzle pressure ratios to identify the origin of a locally re-attached flow condition that was detected in previous test campaigns. A convex shaped Mach disc was found for nozzle pressure ratios less than 10 and a slight concave one for nozzle pressure ratios more than 20. Due to boundary layer transition at low nozzle pressure ratios the convex Mach disc is temporary tilted and redirects the flow towards the nozzle wall. A simple separation criterion for turbulent nozzle flows is presented that fits well for both cold and hot flows. It is shown that the oblique separation shock recompresses the flow to 90% of the ambience. The separation zone of the presented film cooled nozzle is compared with a conventional one around 40% longer. Furthermore a relation between shear layer shape and forced side loads is described. Keywords Flow separation · Ideal contour nozzles · Side loads · Mach disc · Separation criteria PACS 47.32.Ff · 47.40.-x · 47.60.Kz
Communicated by A. Hadjadj. R. Stark (B) · B. Wagner Institute of Space Propulsion, Lampoldshausen, German Aerospace Center, DLR, 74239 Hardthausen, Germany e-mail:
[email protected]
1 Introduction Today’s heavy launch vehicles like Ariane 5, Delta IV or H2 feature a parallel staged configuration where the core stage engines have to fulfil a wide range of operation, starting at sea level up to vacuum condition. To achieve a maximum overall performance it is beneficial to design the supersonic nozzle part with a high area ratio yielding a maximum specific impulse at high altitudes. However this nozzle will be driven over expanded at sea level resulting in thrust losses and a flow that tends to separate from the nozzle wall. Flow separation leads to undesired side loads affecting the nozzle itself, the engine, the actuators, the launchers structure, and the payload. With this background an accurate separation criterion is crucial. Nevertheless flow separation will take place during transient engine start up until the nominal combustion chamber pressure is reached and during engine shut down. The thereby induced typical side loads, caused by the non-uniform moving separation front, can be exceeded by the transition to a flow pattern called restricted shock separation (RSS) where a reattached flow is present. RSS is known to occur in thrust optimized parabola (TOP) nozzles of engines like Vulcain, SSME or J2S. It has been shown experimentally as well as analytically that such a classical reattached RSS flow condition can be excluded in truncated ideal contour (TIC) nozzles [5,12]. However the German Aerospace Center (DLR) showed that another reattached flow phenomena take place at very low nozzle pressure ratios in TIC nozzles as well as in TOP nozzles [8]. This re-attachment was observed to be partial with a random character. To clarify the origin of this reattached flow and to verify the mentioned separation criterion DLR ran a cold flow test series studying the boundary layer separation, the resulting system of oblique separation shock, Mach disc, and triple shock. The results can be compared to
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an existing hot flow separation database and serve as CFD validation cases [16].
2 Test setup The tests were conducted at DLR’s horizontal cold flow test position P6.2 using dry nitrogen as a working fluid, stored in high pressure vessels under ambient conditions. The maximum total pressure and the minimum total temperature were 5.6 MPa and 230 K, respectively. The flow passes a settling chamber, a cross-section constriction, and a bending tube section before it accelerates in the convergent-divergent nozzle to supersonic velocity (Fig. 1). As the storage pressure decreases during a test run the storage temperature and in succession the total temperature of the working fluid decreases, too. From a certain point on the supersonic fluid, due to its low temperature and pressure, will condensate. The flow at low nozzle pressure ratios ( p0 / pa < 10) where oblique shock and Mach disc are located inside the nozzle, was of interest. An acrylic glass TIC nozzle was cut step by step from L/R ∗ = 12 down to L/R ∗ = 1.75, where L is the length of the supersonic nozzle part from the nozzle’s throat to its exit and R ∗ is the throat radius. The nozzle was equipped with up to 50 pressure transducer ports in the stream wise direction with a spacing of 2.5 mm each, starting in the throat. The machine-made contour was checked in three axial planes and the deviation compared to the design was less than 5 µm. The exhaust jet was studied with a color Schlieren setup based on the dissection technique [1,2]. Nozzle and test setup are described in more detail in Frey [4] and Stark and Wagner [17]. All tests follow a profile of a stepwise reduced total pressure, p0 , to provide stationary conditions for the Schlieren imaging. Figure 2 clarifies the determination of the incipient separation. The intersection of the wall pressure profile obtained by a numerical method of characteristics analysis (e.g. with SEA’s TDK) and a tangent along the steepest wall pressure gradient marks both the location of the incipient separation, X sep , and its related lowest wall pressure, psep . Incipient separation means the first deviation from the vacuum wall pressure profile. The distance between incipient separation and real physical flow separation where the wall shear stress is zero defines the separation zone. As it is difficult to determine the physical separation by wall pressure measurements and in order to simplify
Fig. 1 Sketch of horizontal test section
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Fig. 2 Separataion evaluation, L/R ∗ = 9.0, NPR = 25.25
the following discussion, the incipient separation, with its pressure and location, will be defined as separation.
3 Discussion of experimental results 3.1 Flow separation The data obtained with nozzles of different lengths have to be compared regarding the influence of the length on separation location, back pressure, and finally the position and the shape of the Mach disc. Figure 3 shows the averaged separation locations, X sep /R ∗ , of all tested nozzle lengths as a function of the nozzle pressure ratio, p0 / pa , (NPR) where pa is the ambient pressure. The data sets superpose each other following a common linear trend as long as the flow really separates. If a separation zone reaches the related nozzle lip, a continued NPR rise only results in a compression of the separation zone, indicated by a distinct gradient change in separation locations. Two deviations are visible. The obvious one, at around NPR = 30, was due to nitrogen condensation.
Fig. 3 Averaged separation location. Normalized nozzle coordinates versus NPR
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Fig. 4 Averaged separation location. psep / pa versus Masep
Fig. 5 Pressure coefficient versus Reynolds number
The condensation started at the nozzle centre line spreading along a Mach isoline then hitting the nozzle wall. It delays the flow expansion resulting in a down-stream shift of the separation. The inconspicuous deviation at NPR of 5 where a certain down-stream jump of the separation took place. Its origin will be addressed later on. The common trend in Fig. 3 for average separation location allows the conclusion that the nozzle length did not influence the separation location. Therefore the data can be taken as representative of a full length nozzle. Figure 4 plots the separation pressure, psep , as a function of the corresponding wall Mach number, Masep , where the wall Mach number is based on the isentropic ratio p0/psep . The data affected by condensation and the compressed separation zones are not plotted in Fig. 4. An unstable region near wall Mach number of approximately 2.4 (corresponding to the previously discussed low NPR of 5) divides the data-set into two regions. Of practical interest are the wall Mach numbers above 2.5, which is the case in full flowing rocket engines at sea level. Full flowing here means: the boundary layer is attached until the exit plane. The criterion psep 1 = pa Masep
(1)
reproduces this separation pressure data quite well between wall Mach numbers 2.25 and 3.6. The well known Schmucker [14] separation criterion is plotted for comparison to point out the improved prediction with the proposed criterion. The data were sorted by the three determined Mach number regions. Figure 5 presents the corresponding pressure coefficients as a function of the Reynolds number, as presented by Donaldson [3,9,15], who studied supersonic tube flows, where, p2 , is the pressure downstream the shock and, γ , the adiabatic exponent. Included on Fig. 5 are the critical pressure coefficients for turbulent (∼Res−0.2 ) and laminar (∼Res−0.5 ) separation on flat plates. The squares represent the unstable Mach number region around 2.4. With Reynolds numbers of about 106 , which is known to be the laminar-toturbulent transition [13], they split up the remaining data in
Fig. 6 Averaged maximum back pressure
two distinct zones. Separation data for Mach number ≥ 2.5 (circles) shows a clearly turbulent separation behaviour. The separation data for Mach number ≤ 2.25 (diamonds) behave more laminar-like. This leads to the conclusion that the introduced separation criterion (1) is valid for turbulent flows only. Even more: at the low NPR of 5 a transition from laminarlike to a turbulent separation takes place resulting in a downstream shift of the separation. Figure 6 shows a linear correlation between the maximum pressure, pbmax /pa , inside the separated back flow region (Fig. 2) and the separation location. Compared are results of the several times shortened nozzle (61, 73 and 81% of nominal design length). The effective length of the nozzle is negligible and the linear trend of pbmax /pa converges to 0.9 for the full flowing nozzle. This is to say: the oblique separation shock re-compresses the flow to approximately 90% of the ambient pressure and the remaining adaptation to ambient conditions takes place over the free jet. 3.2 Side loads The flow pattern resulting from separation is sketched in Fig. 7. The separation causes an oblique shock directing the flow towards the symmetry axis and adapting it to ambient
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Fig. 9 Triple point, radial position
Fig. 7 Sketch of shock system
Fig. 10 Comparison of triple point and shear layer deflection
Fig. 8 Triple point, axial position
pressure. The shock hits the Mach disc in the triple point and is reflected as the triple shock. The triple shock redirects the flow parallel to the symmetry axis, hits the shear layer, and is reflected as an expansion fan. Figure 8 plots the axial position of the triple point, X tr , as of function of the NPR. This data was obtained from Schlieren images and averaged over all tests. It shows a common trend, except for NPR around 30 where nitrogen condensation took place. Added is a dashed line representing the axial station of the exit plane of the nominal nozzle design. Figure 9 plots the corresponding radial position, Rtr /R ∗ , of the triple point. A distinct common process is found here as well. This leads to the conclusion that the Mach disc, both with its position and size, were not affected by the nozzle length. This data is representative of a shock system located inside a nozzle of nominal design length and can be compared to data already obtained with the nominal TIC nozzle. It is interesting to analyse the position where the triple shock hits the shear layer. At that location the shear layer is redirected and its spatial shape changes from conical to more cylindrical. In Fig. 10 the axial position of this point of contact (circles) is compared to the axial position of the
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triple point (diamonds). The data are averaged from Schlieren images of test series L/R ∗ = 12 to 9 as only here the interesting axial position X/R ∗ = 14.83 is included. Figure 3 verifies a separated flow up to NPR = 37.13. Therefore the shear layer shape is representative of a full length nozzle. The full flowing condition above NPR = 37.13, with its compressed separation zone and lower oblique shock angle, leads to a trend deviation of triple and contact point position. The dashed line marks the exit plane position of nominal design nozzle. For a NPR between 32 and 34 the shear layer deflection overlaps with the exit plane. This means for NPRs 34 with a conical one. The change from one shape to the other is discontinuous. Assuming a fluctuating separation the system of oblique shock, Mach disc, and triple shock will fluctuate, too. Hence the shear layer deflection fluctuates at the nozzles exit plane. Its cross-section discontinuity might couple with the backflow, forcing the separation fluctuation and increasing the side loads. Figure 11 contains the side loads measured in a previous test campaign [8] for a TIC nozzle of nominal design length. The plotted load is equivalent to a force acting at the nozzle lip perpendicular to its symmetry axis. Assuming a correlation between side load and the lever arm of the fluctuating
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Fig. 11 Side loads and shear layer shape change
separation a continuously increasing trend should be expected until a full flowing nozzle is reached. Departure from this trend indicates a change in side load process. Departure is indicated for positive NPR gradient, d p0 /dt > 0, (black) by the distinct peaks around NPR = 25 and 36. For a negative NPR gradient, d p0 /dt < 0, (gray) only one distinct maxima around NPR = 25 arises. This fact is also given in measurements published by Frey [4]. Superimposed is the exhaust jet cross-section, A j , extracted from Schlieren images at the constant axial position of X/R ∗ = 14.83, e.g. the nominal design exit plane, Ae . Scaling by Ae leads to the fraction that is filled by the exhaust jet. The contact point evaluation (Fig. 10) leads one to expect a cross-section discontinuity between NPR = 32 and 34. This discontinuity takes place but it starts slightly before the side loads show their maximum peak. An unexpected significantly more distinct fraction discontinuity appears at NPR = 25. This discontinuity aligns with the previously mentioned side load maxima. This data shows a correlation between the shear layer shape discontinuity and side loads. It is likely that the discontinuities cause a feedback with the fluctuating separation and amplify the side loads. Another objective was to study the side load peaks that occur at low NPR such as those that can be seen in Fig. 11. These low NPR side loads are of the order as the typical mean side load value. Their origin is a, short lived, reattached flow as identified in previous nozzle test campaigns [8]. Some CFD studies [8,10,11] predict a clearly concave Mach disc at moderate NPR. According to Kwan [8] this concave mach disc acts like a cap shock pattern and redirects the flow towards the nozzle wall similar to a restricted shock that appears in TOP nozzles. The Schlieren images from the current test campaign show that the Mach discs never had more than a slight concave curvature, and than, only limited to its centre. Figure 12a shows the maximum observed concave Mach disc. Note that it occurred at a relatively high NPR of around 30. For NPR less than 10 the slight concave shape became convex as shown in Fig. 12b. Therefore, the suggestion that a concave Mach disc, redirecting the flow towards
Fig. 12 Schlieren images a L/R ∗ = 9.0, NPR 30, b L/R ∗ = 1.75, NPR 5.5
Fig. 13 Tilted Mach disc; L/R ∗ = 1.75; NPR = 4.93
the wall, must be excluded as origin of these low NPR side loads. The pressure coefficients (Fig. 5) show that a relaminarized boundary layer is present in the nozzle throat. Thus, the separation zone has to pass, during transient start-up and shut-down, through the transition to turbulence again. Its performance changes and the separation is abruptly shifted downstream. This process is circumferentially asymmetrical and results in a temporary tilted Mach disc, as shown in Fig. 13. In the nozzle of full design length this tilted Mach disc redirects the flow towards the wall. This tilted Mach disc is what induces the partial re-attachment of the flow to the nozzle wall causing large side loads at low NPR. This process is locally limited and reversible as the NPR is further increased. It is a close-limited instability in separation behaviour. 4 Hot flow comparison The introduced separation criterion can be compared with hot flow data obtained within a test campaign called CALO. The hot flow tests were performed in cooperation with ASTRIUM and Volvo Aero [6,7] at DLR’s high pressure test bench P8. The engine was operated using LOX/GH2 with combustion
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full flowing. As the maximal ordinate value marks the nozzle exit plane, the separation zone of the film cooled nozzle can be found to be approximately 40% longer. Separation pressures and separation positions lead to the following: the physical separation of the film cooled nozzle is dominated by the hot gas flow and comparable to the conventional nozzle, but its incipient separation is dominated by the GH2 film and shifted upstream.
5 Conclusion Fig. 14 Hot flow separation pressure versus wall Mach number with and without film cooling
pressures up to 13 MPa. TIC nozzles with and without GH2 film coolant, featuring conditions similar to Vulcain 2, were compared. Figure 14 shows the separation pressures as a function of the related wall Mach number for the conventional cooled and the film cooled TIC nozzle. The wall Mach number of the film cooled nozzle is calculated two different ways; traditional based on the hot gas flow and also based on the pure GH2 coolant conditions. The data of the conventional cooled TIC nozzle (diamonds) fit very well with the suggested criterion 1/Masep . The separation pressures of the film cooled nozzle, based on the hot gas, (circles) indicate a premature separation. However, the separation pressures of the film cooled nozzle, based on the pure GH2 film Mach number (triangles), are much closer to the suggested criterion. Figure 15 plots the axial incipient separation positions, X sep , as function of the NPR for the two nozzles. Both data sets (with and without film) follow a linear trend where the lower values of the film cooled nozzle indicated a premature separation. However, at a NPR around 60 both data sets depart from their linear trend and behave like typical separation zones reaching a nozzle exit plane, being compressed with further on increased NPR (compare Fig. 3). This is to say the real physical flow separation of both nozzles reaches for the same NPR the nozzle exit plane, meaning the nozzles are
Fig. 15 Hot flow separation location with and without film cooling
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The comparison with existing hot flow data demonstrated that the introduced separation criterion, obtained with experimental cold flow studies, is applicable to hot flow separation as well. It is valid for turbulent nozzle flows and, therefore, suitable for technical application to rocket engines. Further it was shown that the physical separation, meaning the hot flow lift off the wall, of film cooled nozzles is comparable to those of conventional nozzles but the separation zone is longer. It was shown that side loads of separated nozzles are forced by the shear layer shape discontinuities passing the nozzle exit plane. The data evaluation showed that a relaminarization of the boundary layer in cold flow rocket nozzle throats is possible. If relaminarization occurs, the transition to a turbulent boundary layer causes, via asymmetric circumferential transition, a tilted Mach disc that redirects the flow towards the nozzle wall resulting in large side loads at low nozzle pressure ratios. These side loads can (depending on the nozzle’s length) exceed the peak load from the rest of the start transient.
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