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Leonardo Times MARCH 2014Internship report
STARTING AT THE FRONT END
When results from complex CFD calcula-tions failed to match the experimental re-sults, the consensus was that errors in up-stream boundary conditions were causing discrepancies downstream. Hence the focus was shifted from the entire flow do-main to only the very first segment. The nozzle core (see Fig. 2) is a piece roughly 10.5 cm in length and contains three segments: a stagnation chamber, a neck region, and an expansion cone. Heated nitrogen gas flows from the heater into the stagnation chamber, where it is sup-posed to homogenise and return to sub-sonic speeds after being rushed through the heater. Then the subsonic flow passes through the nozzle neck, where it reaches Mach 1, and continues to accelerate as it exits through the expansion cone. The is-sues stem from two facts, firstly the “larg-est” piece has a neck diameter of only 1 cm and the maximum stagnation temper-ature of the flow is around 1400 K. Combining these two conditions means that the neck is at risk of being reduced in effective cross-sectional area, as increased
wall temperatures lead to increased boundary layer thickness. To solve this, active cooling is employed on part of the outer surfaces of the nozzle core. This results in a very steep thermal gradient within the nozzle core as well as a tinuous heat flux caused by thermal con-tact with the flow. As inaccurate boundary conditions were thought to be at the root of the discrepancies between simulations and experimental results, the suggested solution was a model utilizing thermal coupling to yield a better temperature boundary conditions, based on simulated temperature fields within the nozzle core pieces. The data from this coupled model had three main questions to answer. What does the temperature profile look like? How sensitive is it to changes? And, does the flow in the stagnations chamber actu-ally stagnate? These questions had to be answered for five different nozzle cores, each with a unique neck diameter, vary-ing material properties and different op-erating conditions.
ADDING PARTS TO SIMPLIFY
The goal of complicating the model by
adding a coupling mechanism is to re-move the uncertainty regarding the con-ditions of the surface being coupled. This, however, leads to additional boundaries and considerations coming into play from the integration of the structural model. To be able to generate a thermal field within the nozzle core piece (see Fig. 3) all the contact surfaces had to be accounted for. Moreover, the nozzle core is exposed to a high current which is used to power the heater and passes through the nozzle piece on its way out. Five boundary seg-ments, induction heating and internal radiation all became active possibilities that had to be either proven negligible or incorporated into the model.
The very low resistivity of the materials used to construct the nozzle cores togeth-er with the relatively large cross-sectional area of the nozzle piece (when compared to the cross-sectional area of the heater) resulted in estimated electric induction heating well below a level that could be considered to be important. Initial runs also showed wall temperatures dropped quickly to levels below 400 K at the throat
Internship assignment at DLR Göttingen
When modelling a supersonic wind tunnel, such as the V2G (see Fig. 1), the
trade-off between affordable computations and accurate results drives much of current
research. In all of DLR’s previous simulation attempts, inconsistencies were found
when compared to the experimental data. To determine where the differences
arose, detailed models of each stage were deemed necessary to validate boundary
conditions. The first stage: the nozzle core.
TEXT Vincent Maes, MSc Student Aerospace Structures and Computational Mechanics
V2G THERMAL COUPLING ANALYSIS
MARCH 2014 Leonardo Times
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and then remained within a bound of roughly 100 K. At such low temperatures and with such small variation in tempera-ture it was concluded that radiation, too, could be ignored. This decision was critical as it allowed for the domain to be reduced to a semi 2D model (CFD calculations re-quire volumes and hence always at least one element in thickness direction) which greatly reduced computational times.
STAGNATION IS KEY
The V2G wind-tunnel is controlled with the help of a thermo-couple that is in-serted into the stagnation chamber of the nozzle cores. The temperature mea-surement made this way is assumed to be the stagnation temperature of the fl ow. Hence, the power supplied to the heater is tuned to get the desired temperature from this measurement. Validity of this technique is dependent on the stagna-tion of the fl ow within the stagnastagna-tion chamber. If the fl ow is not “fully” subsonic (set here to be below Mach 0.2 to 0.3), the measurement will no longer accurately represent the stagnation temperature, calling into question any post analysis done on the data.
The worry that the fl ow may not be sub-sonic arises from the fact that the heater exit has a combined area of roughly 35 mm2 while the largest nozzle core has a
throat area of nearly 80 mm2. This gives
rise to the reasoning that the fl ow coming in from the heater is most likely close to, if not actually, supersonic and comes in as
high fl ow streams that would easily have Mach numbers above Mach 0.3. While the 2D models did confi rm this suspicion, they suff ered from simplifi ed boundary conditions. The actual heater end, shown in Fig. 4, could only be properly captured in 3D models that covered at least an eighth of the total possible domain (this is the smallest piece that can be repeated to recreate the full volume).
From the 3D models it quickly became ap-parent that all expectations were true: the fl ow did enter the stagnation chamber as high speeds (above Mach 0.3) and this re-sulted in recirculation happening within the stagnation chamber. Based on these results a secondary study was launched into the eff ects of redesigning the heater end, in an attempt to improve the condi-tions in the stagnation chamber for the larger pieces.
NARROWING DOWN THE FIELD
While the research into the stagnation chamber fl ow fi eld was interesting and prompted much discussion, it was not in fact the main goal for the project. The ini-tial desired outcome was a better under-standing of the behaviour of the tempera-ture profi le along the wall of the nozzle pieces. As already mentioned, there are several variables that can play a role. A to-tal of more than fi fty coupled simulations were run to assess how the temperature distribution varied. It was found that the heat passed on from the fl ow to the struc-ture was relatively small and as such on
the geometry and boundary conditions set on the structural side were critical. The geometry played a crucial role as for the larger pieces the stagnation chamber is widened which removes material, caus-ing temperatures to rise locally. As such, the geometry of the piece established a baseline shape for the temperature pro-fi le while heater contact temperature and the cooling strength dictated the actual temperatures along the wall. From these fi ndings it was determined and later veri-fi ed that a temperature proveri-fi le could be eff ectively estimated with the use of base profi les for each of the pieces as well as reshaping functions based on the change of the heated and cooled wall conditions.
LOOKING UP AHEAD
Half way through the project, when the fi rst temperature profi les and sensitiv-ity study simulations had been achieved, a second stage project was started to run alongside this one. Another student joined the team and started running sim-ulations of the next section of the wind-tunnel using the temperature profi les pro-vided. That project made great progress and showed good initial agreement with experimental data. Results also showed that the simulation was not as sensitive to wall temperatures as expected. The ques-tion now remains that if not the down-ward boundary conditions caused the deviations between the initial results and the experimental results, then what else caused it?
Figure 3. Temperature fi eld in nozzle as calculated using FEM Figure 1. Picture of the V2G wind tunnel at DLR Göttingen
Figure 4. 3D model of fl ow domain with accurate heater outlet Figure 2. Engineering drawing of the 10 mm nozzle core
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