Si mul ation of a complete re flected shoc k tunnel sho wi ng a vortex mec hani sm for flo w contami nati on. Richard J. Gooz´ ee Department of Mechanical Engineering, The University of Queensland, Queensland, Australia (pres ently at WBM Pty Ltd, Brisba ne) [email protected]Peter A. Jacobs Department of Mechanical Engineering, The University of Queensland, Queensland, Australia [email protected]David R. Buttsworth Faculty of Engineering and Surveying, The University of Southern Queensland, Queensland, Australia [email protected]Communicated by [see published version] Received [see published version] Abstract. Simulations of a complete reflected shock tunnel facility have been performed with the aim of providing a better understanding of the flow through these facilities. In particular, the analysis is focused on the premature contamination of the test flow with the driver gas. The ax- isymmetric simulations model the full geometry of the shock tunnel and incorporate an iris-based model of the primary diaphragm rupture mechanics, an ideal secondary diaphragm and account for turbulence in the shock tube boundary layer with the Baldwin-Lomax eddy viscosity model. Two operating conditions were examined: one resulting in an over-tailored mode of operation and the other resulting in approximately tailored operation. The accuracy of the simulations is as- sessed through comparison with experimental measurements of static pressure, pitot pressure and stagnation temperature. It is shown that the widely-accepted driver gas contamination mecha- nism in which driver gas ‘jets’ along the walls through action of the bifurcated foot of the reflected shock, does not directly transport the driver gas to the nozzle at these conditions. Instead, driver gas laden vortices are generated by the bifurcated reflected shock. These vortices prevent jetting of the driver gas along the walls and convect driver gas away from the shock tube wall and down- stream into the nozzle. Additional vorticity generated by the interaction of the reflected shock and the contact surface enhances the process in the over-tailored case. However, the basic mechanism appears to operate in a similar way for both the over-tailored and the approximately tailored conditions.
Transcript
8/3/2019 Richard J. Goozee, Peter A. Jacobs and David R. Buttsworth- Simulation of a complete re ected shock tunnel showin…
Abstract. Simulations of a complete reflected shock tunnel facility have been performed with theaim of providing a better understanding of the flow through these facilities. In particular, theanalysis is focused on the premature contamination of the test flow with the driver gas. The ax-isymmetric simulations model the full geometry of the shock tunnel and incorporate an iris-basedmodel of the primary diaphragm rupture mechanics, an ideal secondary diaphragm and accountfor turbulence in the shock tube boundary layer with the Baldwin-Lomax eddy viscosity model.Two operating conditions were examined: one resulting in an over-tailored mode of operation andthe other resulting in approximately tailored operation. The accuracy of the simulations is as-sessed through comparison with experimental measurements of static pressure, pitot pressure andstagnation temperature. It is shown that the widely-accepted driver gas contamination mecha-nism in which driver gas ‘jets’ along the walls through action of the bifurcated foot of the reflectedshock, does not directly transport the driver gas to the nozzle at these conditions. Instead, drivergas laden vortices are generated by the bifurcated reflected shock. These vortices prevent jettingof the driver gas along the walls and convect driver gas away from the shock tube wall and down-stream into the nozzle. Additional vorticity generated by the interaction of the reflected shock andthe contact surface enhances the process in the over-tailored case. However, the basic mechanismappears to operate in a similar way for both the over-tailored and the approximately tailoredconditions.
8/3/2019 Richard J. Goozee, Peter A. Jacobs and David R. Buttsworth- Simulation of a complete re ected shock tunnel showin…
The full potential of free piston driven reflectedshock tunnels in high enthalpy operation has not
been reached in practice due to the prematurecontamination of the test flow with the driver gas(Stalker and Crane, 1978).
Over the years, various analytical and empir-ical models have been developed in an attemptto predict driver gas contamination (Stalker andCrane, 1978; Skinner, 1994; Paull, 1996), but theyhave never been successful across a range of op-erating conditions. Attempts at understandingdriver gas contamination have been based on themechanism first described by Mark (1957). Mark(1957) observed that the reflected shock can bi-
furcate as it moves upstream through the shocktube boundary layer and that the gas emergingfrom the two oblique shocks at the bifurcated footcan have a higher velocity than the gas that passesthrough the normal shock. Burtschell et al. (2001)stated that the driver gas that passes through thisbifurcated region penetrates into the test gas asa jet along the tube wall to contaminate the testflow; however, this phenomenon appears to be in-capable of explaining the observations of contami-nation in previous experimental studies (Skinner,1994; Cardoso et al., 1997).
To improve the understanding of key shocktunnel processes such as contamination, axisym-metric numerical simulations have been used(Sharma and Wilson, 1995; Wilson, 1995; Chueand Eitelberg, 1998); however, previous axisym-metric simulations of reflected shock tunnels havegenerally modelled only particular parts of a facil-ity. Typically the very end of the shock tube andthe nozzle have been modelled using inflow con-ditions derived from empirical relations (Sharmaand Wilson, 1995; Wilson, 1995). The results ob-tained in these simulations are heavily depen-
dent on the assumptions associated with mod-elling only part of a facility. Axisymmetric simu-lations have also aimed specifically at modellingthe interaction of the reflected shock with theboundary layer, for the purpose of interpretingits effect on flow contamination by the driver gas(Wilson, 1995; Badcock, 1992). Chue and Eitel-berg (1998) noted the generation of vorticity inthe driver gas interface during its interaction withthe reflected shock; however, the process was notfollowed through its complete evolution and it wasconcluded that this vorticity would act to post-pone contamination.
The simulations described in this paper rep-resent a contribution beyond that of previous ax-isymmetric reflected shock tunnel simulations be-cause a complete facility from the driver section
to the dump tank has been simulated. This issignificant because it transpires that contamina-tion of the test gas occurs through the combina-tion of a number of mechanisms that occur dur-ing the evolution of the flow along the length of the shock tunnel. Thus, identification of the ac-tual contamination mechanisms is more likely tobe achieved through complete tunnel simulationsthan by modelling parts of the facility in isolation.
The simulations are validated by comparingthe temporal variation of simulated flow quantitieswith experimental measurements at particular lo-
cations within the shock tunnel for the two oper-ating conditions. As with previous axisymmetricsimulations (Sharma and Wilson, 1995; Wilson,1995), experimental benchmarking is achieved us-ing reflected shock tunnel data for relatively lowenthalpy conditions to avoid the complication of thermochemical effects experienced with high en-thalpy operation. Having assessed the accuracyof the simulations, results are then presented toillustrate the simulated driver gas contaminationmechanisms observed for the two shock tunnel op-erating conditions.
2. Overview of the Simulations
The simulations described in this paper modelthe flow through the Drummond Tunnel, whichis a relatively low enthalpy reflected shock tun-nel operated within the Centre for Hypersonicsat the University of Queensland (Austin et al.,1997; Craddock et al., 1998). Figure 1 illustratesthe Drummond Tunnel facility and the associatedinstrumentation. Although the tunnel produces a
relatively low enthalpy flow, it can still be used toinvestigate the fluid mechanics that operate in amodified form at higher enthalpies. Data from thistunnel can also be used to establish whether drivergas contamination can be predicted by numericalsimulations of complete facilities. The simulationsare provided with only the geometry and the ini-tial tube filling and boundary conditions from theoperation of the real facility and are run from theinitiationof therupture of theprimary diaphragm.
The simulations were performed using themulti-block CFD code, MB CNS (Jacobs, 1996),
8/3/2019 Richard J. Goozee, Peter A. Jacobs and David R. Buttsworth- Simulation of a complete re ected shock tunnel showin…
Simulation of a complete reflected shock tunnel showing a vortex mechanism for flow contamination. 3
pressuretransducer
68
Mach 4
conical
nozzle
test section anddump tank
driver shock tube
primarydiaphragm
secondarydiaphragm
probes
3013, 62.2dia1000, 59dia
pneumaticcylinder and
piercer
pressuretransducer
68
secondarydiaphragm
62.2 22.2
70.0
nozzle centre line
14
14
8deg
83 17
pitot probe
temperature probe
alumel wire
chromel wire:
0.8 OD
alumel
annulus
nichromeheating wire:
0.2 OD
ceramic tube:2.0 OD, 1.0 ID
2.0 dia
insulation 0.02
weld
quartz transducer
baffle
inlet
Figure 1. Illustration of the reflected shock tunnel arrange-ment and associated instrumentation. Dimensions are inmm.
which is based on a finite-volume formulation of the compressible Navier-Stokes equations. It hasa shock-capturing capability through the use of a limited reconstruction scheme and an adaptiveflux calculator that switches from AUSM (Wada
and Liou, 1994) to the Equilibrium Flux Method(EFM) (Macrossan, 1989) where large velocitygradients are detected.
An axisymmetric, body-fitted mesh is used torepresent the geometry of the complete facility, in-cluding the driver section, the length of the shocktube, the Mach 4 nozzle, the test section and thedump tank. The axisymmetric approach allowsa good representation of the cylindrical geome-try of the shock tunnel, but prevents circumfer-ential motion or gradients. This approximationis used because it affords considerable computa-
tional savings relative to fully three dimensionalmodelling, but has the effect of forcing artificiallyhigh levels of coherence in vortical structures. Themeshes were refined towards the walls, to resolvethe boundary layer, and towards regions wherethe geometry of the shock tube changed.
Two refinements of the original (coarse) meshwere used for convergence studies. The numberof cells across the radius of the shock tube wasvaried from 40 cells for the coarse mesh, to 60cells for the medium mesh and 80 cells for the finemesh. These three meshes consisted of a total of
80,850 to 181,980 and 323,400 cells respectively.Analysis of the simulated flow field produced withthese meshes showed that there was an adequatelevel of convergence in the results produced with
the finest mesh. The simulated results and imagespresented in this paper were obtained using thefine resolution mesh. Further details on the meshrefinement studies are available in Goozee (2003).
The simulation of a complete experimental testin a shock tunnel requires the simulation of highspeed transient flow for a significant period of time. This means that the large mesh sizes arecombined with the requirement for marching thesolution over large numbers of time steps. Suchlarge scale simulations have been made possi-ble through the use of parallel processing super-
computing. The meshes were decomposed into 24blocks in order to represent the geometry of thefacility and to allow parallelisation of the solution.
A constant temperature of 296 K (equal to theambient temperature) was specified at the wallboundaries because only small changes (typicallyless that 5 K) in surface temperature occur overthe period of interest during the experiments.Since all of the gases used in the facility are mod-elled, there are no gas inflow or outflow boundariesin the simulation.
The peak temperatures in the stagnation re-gion at the end of the shock tube remain below1600 K. At these temperatures, vibrational modesof excitation of the nitrogen molecules are not yetsignificant. For the Helium driving Nitrogen case,the gas model assumed that the gas was a mixtureof perfect gases. For the Nitrogen driving Nitrogencases, a look-up table, based on the CEA program(Gordon and McBride, 1994; McBride and Gor-don, 1996) was used.
The properties of gases composed of multiplecomponents (or species) are modelled by solving
additional equations for conservation of each of these component gases. The properties of the gasmixture in each cell can then be calculated usingmass fraction weighted averages of the componentgas properties.
The flow in the real facility is initiated by therupture of an aluminium diaphragm separatingthe driver gas from the driven gas. In order toobtain an adequate simulation of the performanceof the actual shock tunnel, it was necessary toaccount for the finite opening time of the primarydiaphragm. The primary diaphragm was assumed
8/3/2019 Richard J. Goozee, Peter A. Jacobs and David R. Buttsworth- Simulation of a complete re ected shock tunnel showin…
to rupture with a linear profile of opened cross-sectional area versus time that was derived fromthe experiments of Rothkopf and Low (1974). Theradius of the opening diaphragm was increased at
each time step, until the final radius (identifiedfrom measurements on spent Drummond Tunneldiaphragms) was reached.
The Drummond Tunnel also has a thin sec-ondary diaphragm, which initially separates thetest gas from the dump tank section. Follow-ing the arrival of the shock at the secondary di-aphragm, the pressure rises rapidly and the di-aphragm bursts within a very short period. Inthese simulations the secondary diaphragm is as-sumed to rupture instantaneously and completelywhen a specified pressure rise occurs at its up-
stream face.
The simulations initially modelled the bound-ary layers as laminar. These simulations signifi-cantly over-estimated the incident shock pressure.The accuracy of the simulations was improvedby accounting for the effect of turbulence in theboundary layerson the shock tube wall and nozzle.The Baldwin-Lomax eddy viscosity model (Bald-win and Lomax, 1978) was used. The model iscomputationally inexpensiveand robust; however,it is an incomplete turbulence model and requiresknowledge of the flow conditions being modelled
in the form of modifiable coefficients.
3. Experimental Validation
The simulations that are described in this paperreproduced the initial conditions of two sets of ex-periments that were performed in the DrummondTunnel facility, one resulting in over-tailored andthe other in approximately tailored operation.Theinitial conditions of the simulations were specifiedto match the initial tube filling conditions used inthese experiments, as given in Table 1.
Table 1. The two filling conditions.
Driver Shock tube Level of tailoring
N2 N2 over-tailored
3.25MPa 30.0kPa
He N2 approximately tailored
5.60MPa 61.4kPa
The tube filling pressures were known from theexperiments (as shown in Table 1), but it was laterfound that the initial temperature of the driver gaswould have been somewhat higher than the am-
bient temperature (296K) depending on the rateat which the driver section was filled and the de-lay before the experiment. Since the actual drivergas temperature immediately prior to diaphragmrupture was not measured, the initial tempera-ture of the driver gas in the simulation was tunedwithin the subsequently measured limits of 303and 313 K until the incident shock speed matchedthat of the experiment. The ambient temperatureof 296 K was used as the initial temperature of theshock tube (driven) and dump tank gases becausethere was sufficient time prior to the primary di-aphragm rupture to achieve thermal equilibrium.
The experiments provided sets of measureddata which were used to validate the numericalsimulations. Data were recorded during the exper-iments by a pressure transducer on the wall of theshock tube in the stagnation region near the end of the shock tube and by a pitot pressure probe thatwas located close to the exit plane of the Mach 4nozzle. The arrangement of the instrumentationis shown in Figure 1. In the over-tailored case,a stagnation temperature probe (Buttsworth andJacobs, 1998) was used to provide additional val-idation data. Unfortunately the stagnation tem-perature probe was not available for use in theapproximately tailored experiments which wereconducted as a separate campaign from the over-tailored experiments. Simulated data traces werealso recorded at corresponding locations through-out the simulations.
Figure 2 shows a comparison between the sim-ulated and the experimentally measured nozzlesupply static pressure traces for the over-tailoredcase. For all of the comparisons between the simu-lated and experimental data presented in this pa-
per, the time scale for both the simulated and ex-perimental results is referenced to the arrival of theincident shock at the nozzle supply pressure trans-ducer. The traces show that the simulation repro-duces the conditions behind both the incident andreflected shocks, although there is a deviation be-tween about 0.6 and 0.8 ms on the timescale inFigure 2. This deviation, which occurs when thebifurcated foot of the reflected shock passes overthe transducer, has been noted in previous sim-ulations of reflected shock-boundary layer inter-actions (Weber et al., 1995). The overall rate of pressure rise associated with the over-tailoredcon-
8/3/2019 Richard J. Goozee, Peter A. Jacobs and David R. Buttsworth- Simulation of a complete re ected shock tunnel showin…
Simulation of a complete reflected shock tunnel showing a vortex mechanism for flow contamination. 5
ditions (between about 1.2 and 3.0 ms) is repro-duced by the simulations; however, the simulatedpressure rise proceeds via wave processes that aremore discrete than observed experimentally.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 0.5 1 1.5 2 2.5 3 3.5
S t a t i c P r e s s u r e ( M P a )
Time (ms)
ExperimentTurbulent Simulation
Figure 2. Comparison between the simulated (solid) andexperimentally measured (dashed) nozzle supply pressuretransducer traces for the over-tailored case.
Figure 3 shows a comparison between the simu-lated and the experimentally measured pitot pres-sure traces forthe over-tailoredcase. Thearrival of the nozzle startup waves occurs at approximately0.35 ms and the test flow is not established untilabout 0.7 ms. The simulations accurately repro-duce the test flow pitot pressure and the steadytest time. The arrival time of the pressure rise as-sociated with the over-tailoring (at about 1.55 mson this scale) is reproduced; however, as with thenozzle supply pressure history, the over-tailoringpressure waves are more discrete in the simulationthan in the real flow.
-50
0
50
100
150
200
250
300
0 0.5 1 1.5 2 2.5
P i t o t P r e s s u r e ( k P a )
Time (ms)
ExperimentTurbulent Simulation
Figure 3. Comparison between the simulated (solid) andexperimentally measured (dashed) test flow pitot pressuretraces for the over-tailored case.
Figure 4 shows the data obtained from thestagnation temperature probe, which provides adirect indication of driver gas arriving in the testflow for the over-tailored case. This figure shows
that the driver gas arrives at the stagnation tem-perature probe at about 2.2 ms. The simulationreproduces the arrival time of the driver gas towithin approximately 0.1 ms. This result supportsthe assertion that the essential fluid mechanics,and in particular, the driver gas dynamics, is be-ing modelled with sufficient accuracy. A differenceof 0.1 ms amounts to a spatial error of less than15 mm (about one quarter of the tube diameter)at the average convection velocity of the maincontaminating structure in the end of the shocktube.
The dip in the experimentally measured pitotpressure (Figure 3) at about 2.2 ms is presumablyassociated with the arrival of the cold driver gasin the test section given the decrease in the exper-imental stagnation temperature data at this sametime (Figure 4). The simulated pitot pressure doesnot exhibit such a dip, nor is one expected at thistime since the nozzle exit Mach number shouldremain largely unchanged with the arrival of thecold gas meaning the pitot pressure should varyonly with the nozzle supply pressure in this case.We suggest the dip in the experimentally mea-sured pitot pressure is a consequence of the inter-
action of the transient flow and the probe (whichwas not simulated), and the response time of thepitot probe (see Figure 1) which is around 0.1 ms.
0
200
400
600
800
1000
1200
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
S t a g n a t i o n T e m p e r a t u r e ( K )
Time (ms)
ExperimentTurbulent Simulation
Figure 4. Comparison between the simulated (solid) andexperimentally measured (dashed) nozzle exit stagnationtemperature for the over-tailored case. The dip in stag-nation temperature at around 2.2 ms corresponds to thearrival of driver gas in the test flow.
8/3/2019 Richard J. Goozee, Peter A. Jacobs and David R. Buttsworth- Simulation of a complete re ected shock tunnel showin…
Figures 5 and 6 compare the simulated andthe experimentally measured pressure traces forthe approximately tailored case. Apart from de-viations associated with the bifurcated reflected
shock (between about 0.45 and 0.7 ms in Figure 5),the simulation reproduces the incident and re-flected shock static pressures. The resulting testflow pitot pressure is also reproduced quite well.The test time, being defined as the duration overwhich approximately constant pressure conditionsare produced is likewise simulated accurately. Theoverall decrease in pressure after 1 ms, ending thetest time, is simulated with reasonable accuracyfor both the nozzle supply static pressure (Fig-ure 5) and the nozzle exit pitot pressure (Fig-ure 6). This pressure decrease is associated withthe arrival of the expansion that has reflected fromthe upstream end of the driver tube, rather thantailoring effects.
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.5 1 1.5 2
S t a t i c P r e s s u r e ( M P a )
Time (ms)
ExperimentTurbulent Simulation
Figure 5. Comparison between the simulated (solid) andexperimentally measured (dashed) nozzle supply pressuretransducer traces for the approximately tailored case.
The overall pressure levels and the rates of change of pressure have been simulated with rea-
sonable accuracy. The primary differences be-tween the simulated and experimental results are:1) the bifurcated foot of the reflected shock pro-duces a simulated pressure rise via discrete struc-tures that are not observed experimentally; and2) the simulated disturbances following the in-teraction of the reflected shock with the incidentcontact surface (in particular, the tailoring wavesin the over-tailored case) are also of a larger mag-nitude and more discrete nature than observedexperimentally. These differences are believed tobe associated with the simulation maintaining un-realistically high levels of structural coherence,
-100
0
100
200
300
400
500
600
700
800
900
0 0.5 1 1.5 2 2.5
P i t o t P r e s s u r e ( k P a )
Time (ms)
ExperimentTurbulent Simulation
Figure 6. Comparison between the simulated (solid) andexperimentally measured (dashed) test flow pitot pressuretraces for the approximately tailored case.
since no allowance has been made for either cir-cumferential variations or turbulent diffusion inthe contact surface. Despite the differences at-tributable to structural coherence in the simula-tions, it should still be possible to learn somethingabout the relevant contamination mechanisms be-cause the flow stagnation temperature results pro-vide independent evidence that the time of con-tamination is accurately simulated, at least in theover-tailored case.
4. Over-Tailored Mode Interaction
Figure 7 shows a sequence of the interaction of the reflected shock with the incident contact sur-face for the over-tailored case (Nitrogen drivingNitrogen). Numerical Schlieren images are shownin the upper half of the frames and mass-fractionsare shown in the lower half of the frames (withdriver gas in blue and driven gas in yellow). Thetimes associated with each frame are relative tothe time at which the primary diaphragm rupture
process was initiated.
The first frame in Figure 7 (at 4600 µs) showsthe incident contact surface and the bifurcated re-flected shock. The structure of the shock reflectedfrom the nozzle contraction assumes the formshown in Figure 7 within a distance of about onetube radius upstream of the contraction (Goozee,2003).1
1 Animations showing the flow development during di-aphragm rupture and the reflected shock interactions canbe accessed via http://www.mech.uq.edu.au/cfcfd/
8/3/2019 Richard J. Goozee, Peter A. Jacobs and David R. Buttsworth- Simulation of a complete re ected shock tunnel showin…
Simulation of a complete reflected shock tunnel showing a vortex mechanism for flow contamination. 7
The diaphragm rupture model has a stronginfluence on the contact surface shape andits evolution along the shock tube. When aninstantaneously-removed diaphragm model is
used in the simulations, the contact surface ap-pears stable because it is essentially planar acrossthe inviscid region of the shock tube diameter(Goozee, 2003). Rayleigh-Taylor stability of thecontact surface is confirmed by examining the den-sities and acceleration of the interface: the ex-panded driver gas has a higher density than thedriven gas (around 3.7kg/m3 as compared with1.1kg/m3), and the contact surface acceleratesslightly (at about 4.8×103 m/s2) as it movesdownthe shock tube. However, when the iris diaphragmrupture model is used (as was the case for Fig-ure 7), the driver gas initially appears as an an-nular tongue of material penetrating the drivengas. This simulated contact surface shape differsfrom the conventional picture of a stable inter-face in that the leading edge is not on the cen-tre line of the tube. The observed shape of thesimulated contact surface has its origins in thediaphragm rupture process and the flow devel-opment downstream of the primary diaphragmstation. Our simulations indicate that an obliqueshock structure with a Mach disk on the centreline of the tube is established soon after diaphragmrupture (Goozee, 2003). This leads to lower flow
speeds on the centre line of the tube which is con-sistent with previous simulations incorporating adiaphragm rupture process (Cambier et al., 1992;Petrie-Repar, 2000).
As the reflected shock moves back upstream,the boundary layer does not have enough mo-mentum to cross the normal shock, and insteadboundary layer material builds up at the foot of the shock and is carried with it. This causes theflow to separate, and the shock to bifurcate intoa lambda structure (Mark, 1957). The reflectedshock-contact surface interaction begins at ap-
proximately 4700µs, between the first and secondframes presented in Figure 7. In these frames itis clear that a series of vortices is produced in thetest gas boundary layer by the bifurcated foot of the reflected shock, prior to the reflected shock-contact surface interaction.
It is difficult to draw definite conclusions re-garding the strength of the bifurcated shock rela-tive to that observed in other works because differ-ent visualisation techniques that have been used.Furthermore,in the numerical Schlieren algorithmwe have used, the density gradients have been nor-
malised by the instantaneous maximum densitygradient in each frame so as to avoid image satu-ration. Thus temporal variations in the grey-scaleof particular features may not give reliable quan-
titative information.The driver gas predominantly moves through
the oblique shocks near the shock tube walls(4800µs frame). Vorticity is generated at the con-tact surface during its interaction with the re-flected shock due to the baroclinic torque resultingfrom the misalignment of the pressure and den-sity gradients. By the frame at 5000 µs, the drivergas at the head of the contact surface has movedtowards the shock tube wall. Some driver gas isentrained into the test gas vortex structures, butsignificantly, a large fraction is driven back away
from the shock tube walls and towards the noz-zle (frames 5200 and 5400µs). A vortex is seen toseparate from the head of the driver gas structurenear the shock tube centreline (frames 5600 and5800µs), and the contaminating driver gas accel-erates along the centreline of the shock tube andinto the nozzle throat (frames 6000 and 6200µs).This mechanism causes the driver gas to arrive inthe test flow prematurely here and is possibly themechanism that causes driver gas to arrive prema-turely in the test flow for over-tailored conditionsin other facilities (Sudani et al., 2000).
It is important to note that the length to di-ameter aspect ratio of the compressed slug of testgas in this work is substantially larger than fortypical (higher enthalpy) experiments in other fa-cilities. The length of the compressed slug of testgas may affect the relative significance of the ‘vor-tex’ and ‘wall-jetting’ mechanisms because whenthe driver gas interface is closer to the end of theshock tube, jetting of the driver gas may reachthe end of the shock tube before the vortices havetime to develop.
5. Tailored Mode Interaction
Figures 8 and 9 show the interaction of the re-flected shock with the incident contact surface forthe approximately tailored case (Helium drivingNitrogen). Numerical Schlieren images are shownin the upper half of the frames and mass fractionsare shown in the lower half of the frames (withthe Helium driver gas in blue and the Nitrogendriven gas in yellow). The times associated witheach frame are relative to the time at which theprimary diaphragm rupture process was initiated.
8/3/2019 Richard J. Goozee, Peter A. Jacobs and David R. Buttsworth- Simulation of a complete re ected shock tunnel showin…
Figure 7. Sequence of numerical Schlieren images (top) and Driver gas mass fractions (bottom) showing the over-tailoredinteraction of the reflected shock with the contact surface and the subsequent contamination process.
8/3/2019 Richard J. Goozee, Peter A. Jacobs and David R. Buttsworth- Simulation of a complete re ected shock tunnel showin…
Simulation of a complete reflected shock tunnel showing a vortex mechanism for flow contamination. 9
The first frame, at 3100 µs, shows the inci-dent contact surface and the reflected shock atthe starting instant of their interaction. As withthe over-tailored case, the diaphragm rupture
model has a strong influence on the contact sur-face shape and its evolution along the shock tube(Goozee, 2003). However in this case, the simu-lations indicate that the contact surface is unsta-ble: a distorted interface is obtained even whenan instantaneously-removed diaphragm is used;the expanded driver gas has a density of around2.5kg/m3, thecompressed driven gas has a densityofaround2.9kg/m3, andthe contact surface accel-eratesalong the shock tube at about 35×103 m/s2.(Note that although the simulations indicate thatthis operating condition is slightly under-tailored– the density is lower in the driver gas by about10 % – we havechosen to call it ‘approximately tai-lored’ because there is no clear evidence of expan-sion waves arising from under-tailored operationin the nozzle supply pressure history, Figure 5.)
In contrast with the over-tailored case, mul-tiple discrete vortices are not apparent in thedriven gas; only a single vortex appears to beproduced in the driven gas boundary layer priorto the reflected shock-contact surface interaction.This vortex structure (most clearly seen in frame3200µs) continues to develop over later frames
and propagates along the shock tube ahead of thedriver gas. A number of vortex structures are gen-erated in the driver gas boundary layer as the bi-furcated reflected shock moves upstream (frames3280to3440µs). Themotion causedby this vortic-ity is in a direction as to stop the jetting generatedby the shock foot, as similarly observed by Chueand Itoh (1995); Chue and Eitelberg (1998). Thisis a tailored contact surface interaction and thusthe bulk of the driver gas does not continue tomove downstream immediately following interac-tion with the reflected shock. However, contam-
ination is effected by vortex structures breakingaway from the bulk of the driver gas and propa-gating downstream through the nozzle.
Figure 10 completes the description of the con-tamination process in the approximately tailoredcase by showing a sequence of driver gas mass frac-tion frames for later times in the end of the shocktube, the Mach 4 nozzle and the test section. Thelarge vortex structure identified in frames 3440to 3560µs of Figure 9 is the main contaminatingvortex that separates from the bulk of the drivergas in frames 3720 to 3880 µs of Figure 10.
As was the case with the over-tailored simula-tions, contamination is produced by vortical struc-tures that propagate downstream away from theshock tube walls. These structures then accelerate
through the centreline of the nozzle, contaminat-ing the core test flow. There remains a significantportion of largely uncontaminated test gas in theshock tube after the initial contaminating struc-ture is swept through the nozzle (frame 4520µs).
6. Conclusions
The premature contamination of shock tube testgas with the driver gas is a ubiquitous prob-lem that limits the practical operating envelope
of shock tunnels to enthalpies (or test times)well below theoretical limits predicted by analyt-ical techniques. Progress towards understandingshock tunnels flows and in particular, the problemof contamination, can be achieved through nu-merical simulation with supporting experiments.A complete shock tunnel facility has been simu-lated using an axisymmetric Navier-Stokes solverto avoid restrictive assumptions associated withsimulating only part of a facility. Two operatingconditions have been considered: one over-tailoredthe other approximately tailored.
By incorporating an iris-based model for theopening process of the primary diaphragm and aturbulent boundary layer on the shock tube wall,we have achieved agreement (typically to withina few percent) between the simulated and experi-mentally measured pressure levels behind the in-cident and reflected shocks. The simulated shockspeeds and the rates of pressure change associ-ated with either the tailoring waves or the re-flected driver gas expansion fan are likewise sim-ulated with sufficient accuracy to further supportthe conclusion that the simulations are capturing
the essential fluid mechanics.
There is some discrepancy between the simu-lated and experimental pressure histories associ-ated with the transit of the bifurcated reflectedshock past the shock tube pressure transducer: thesimulated pressure rise takes place through a se-quence of discrete jumps that are not observed ex-perimentally. Such differences have been noted inother axisymmetric shock tube simulations (Wil-son, 1995). A similar sequence of discrete pres-sure waves is simulated in the over-tailored casethrough the interaction of the reflected shock and
8/3/2019 Richard J. Goozee, Peter A. Jacobs and David R. Buttsworth- Simulation of a complete re ected shock tunnel showin…
Simulation of a complete reflected shock tunnel showing a vortex mechanism for flow contamination. 13
the contact surface; again, such discrete pressurechanges are not observed experimentally. Theseeffects are attributed to the artificially high levelsof structural coherence that are being enforced by
the axisymmetric simulations and the absence of turbulent mixing at the contact surface.
Even though these limitations will have someinfluence on the simulation of contamination, wesubmit that useful information on the relevantmechanisms can still be derived from the simula-tions. Support for this contention is drawn fromthe simulation of nozzle exit stagnation temper-ature data in which the time of contamination iscorrectly simulated to within 0.1 ms, correspond-ing to an error in position of the contaminatingstructure’s leading edge of less than one quarter
of the tube diameter.The simulations indicate that the bifurcated
foot of the reflected shock, resulting from the in-teraction of the reflected shock with the bound-ary layer, does cause some jetting of gas as thereflected shock moves through the test gas. How-ever, sustained jetting leading to test flow con-tamination is not observed because the vorticesgenerated in the driven gas as it passes throughthe shock structure act to impede the jetting pro-cess. In the over-tailored case, additional vorticityof the same sign is generated at the interaction of
the reflected shock and contact surface, and thissimilarly impedes the jetting process.
In the over-tailored case, vortices generatedin the driven (test) gas boundary layer combinewith the vorticity deposited at the contact surfaceduring its interaction with the reflected shock topush driver gas away from the shock tube wall.The driver gas is then convected along the nozzlecentreline, completing the contamination process.In the approximately tailored case, the interac-tion of reflected shock and contact surface makeslittle contribution to the generation of vorticity
(since the driver and driven gas densities are al-most matched). However, the vortices generatedin the shock tube boundary layer producea similarcontamination mechanism to that observed in theover-tailored case – they project driver gas awayfrom the wall and towards the nozzle. In the ap-proximately tailored case, a substantial fractionof test gas remains in the shock tube after thecontaminating driver gas structure first appearsat the nozzle exit.
Attempting to extend the duration of the testflow through the addition of an annular gas-bleed
arrangement in the shock tube (as has been donepreviously, for example by Sudani et al. (2000))is unlikely to be successful at these conditions be-cause the contaminating structures appear to be
convected into the nozzle along the tube centre-line. A particle trap arrangement on the shocktube centreline was investigated by Chue and Eit-elberg (1998). Modification of such a device toincorporate a gas bleed has better prospects fordelaying contamination at the conditions we havestudied.
Acknowledgements
Richard Goozee was supported by an Australian
Postgraduate Award. Computing infrastructurewas provided by the Queensland Parallel Super-computing Foundation and the Australian Part-nership for Advanced Computing.
References
J. M. Austin, P. A. Jacobs, M. C. Kong, P. Barker, B. N.Littleton, and R. Gammie. The small shock tunnel fa-cility at UQ. Department of Mechanical EngineeringReport 2/1997, The University of Queensland, Bris-
bane, July 1997.K. J. Badcock. A numerical simulation of boundary layer
effects in a shock tube. International Journal for Nu-merical Methods in Fluids, 14:1151–1171, 1992.
B. S. Baldwin and H. Lomax. Thin layer approximationand algebraic model for separated turbulent flows. InAIAA 16th Aerospace Sciences Meeting , Huntsville,Alabama, 1978. AIAA Paper 78-257.
Y. Burtschell, M. Cardoso, and D. E. Zeitoun. Numer-ical analysis of reducing driver gas contamination inimpulse shock tunnels. AIAA Journal , 39(12):2357–2365, 2001.
D. R. Buttsworth and P. A. Jacobs. Total tempera-ture measurements in a shock tunnel facility. InM. C. Thompson and K. Hourigan, editors, 13th Aus-
tralasian Fluid Mechanics Conference, pages 51–54,Melbourne, December 1998.
J. L. Cambier, S. Tokarcik, and D. K. Prabhu. Numeri-cal simulations of unsteady flow in a hypersonic shocktunnel facility. In AIAA 17th Aerospace ground testing conference, pages 127–140, Nashville, TN, July 1992.
M. Cardoso, Y. Burtschell, D. Zeitoun, and R. Abgrall.Numerical simulation of different methods for avoid-ing driver gas contamination in shock tunnels. In Pro-ceedings of the 21st International Symposium on Shock Waves, Volume 1, pages 537–542, Great Keppel, Aus-tralia, 1997. Panther Publishing.
R. S. M. Chue and G. Eitelberg. Studies of the transientflows in high enthalpy shock tunnels. Experiments in Fluids, 25:474–486, 1998.
8/3/2019 Richard J. Goozee, Peter A. Jacobs and David R. Buttsworth- Simulation of a complete re ected shock tunnel showin…
14 R. J. Goozee, P. A. Jacobs and D. R. Buttsworth
R. S. M. Chue and K. Itoh. Numerical analysis of reflectedshock/boundary layer interaction in a high enthalpyshock tunnel. In Proceedings of the 20th International Symposium on Shock Waves, California Institute of Technology, Pasadena, California, 1995. World Scien-
tific Publishing.C. S. Craddock, P. A. Jacobs, andR. Gammie. Operational
instructions for the small shock tunnel at UQ. Depart-ment of Mechanical Engineering Report 8/1998, TheUniversity of Queensland, Brisbane, July 1998.
R. J. Goozee. Simulation of a complete shock tunnel with parallel computer codes. PhD thesis, The University of Queensland, Brisbane, Queensland, Australia, 2003.
S. Gordon and B. J. McBride. Computer program for cal-culation of complex chemical equilibriumcompositionsand applications I. Analysis. Reference Publication1311, NASA, October 1994.
P. A. Jacobs. MB CNS: A computer program for the sim-ulation of transient compressible flows. Department of Mechanical Engineering Report 10/1996, The Univer-
sity of Queensland, Brisbane, October 1996.M. N. Macrossan. The equilibrium flux method for the
calculation of flows with non-equilibrium chemical re-actions. Journal of Computational Physics, 80(1):204–231, 1989.
H. Mark. The interaction of a reflected shock wave withthe boundary layer in a shock tube. Journal of theAeronautical Sciences, April:304–306, 1957.
B. J. McBride and S. Gordon. Computer program for cal-culation of complex chemical equilibriumcompositionsand applications II. Users manual and program de-scription. Reference Publication 1311, NASA, June1996.
A. Paull. A simple shock tunnel driver gas detector. Shock Waves, 6(5):309–312, 1996.
P. J. Petrie-Repar. Numerical simulation of diaphragm rupture. PhD thesis, The University of Queensland,Brisbane, Queensland, Australia, 2000.
E. M. Rothkopf and W. Low. Diaphragm opening processin shock tubes. The Physics of Fluids, 17(6):1169–1173, 1974.
S. P. Sharma and G. J. Wilson. Test times in hypersonicshock tubes. In AIAA 33rd Aerospace Sciences Meet-ing and Exhibit , Reno, Nevada, 1995. AIAA Paper 95-0713.
K. A. Skinner. Mass spectrometry in shock tunnel exper-iments of hypersonic combustion . PhD thesis, TheUniversity of Queensland, Brisbane, Queensland, Aus-tralia, 1994.
R. J. Stalker and K. C. A. Crane. Driver gas contamina-
tion in a high-enthalpy reflected shock tunnel. AIAAJournal , 16:277–278, 1978.
N. Sudani, B. Valiferdowsi, and H. G. Hornung. Testtime increase by delaying driver gas contamination forreflected shock tunnels. AIAA Journal , 38(9):1497–1503, 2000.
Y. Wada and M. S. Liou. A flux splitting scheme withhigh-resolution and robustness for discontinuities. InAIAA 32nd Aerospace Sciences Meeting , Reno, NV,1994. AIAA Paper 94-0083.
Y. S. Weber, E. S. Oran, J. P. Boris, and J. D. Anderson Jr.The numerical simulation of shock bifurcation near theend wall of a shock tube. Physics of Fluids, 7:2475–2488, 1995.
G. J. Wilson. Numerical studies of high-enthalpy impulsefacilities. In Proceedings of the 20th International Sym-posium on Shock Waves (Volume 1), California Insti-tute of Technology, Pasadena, California, 1995. WorldScientific Publishing Co. Pty. Ltd.
