COMPUTATIONAL STUDIES OF THE VIRGINIA TECH HYPERSONIC WIND TUNNEL

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1 COMPUTATIONAL STUDIES OF THE VIRGINIA TECH HYPERSONIC WIND TUNNEL Rui Chen Deartment of Aerosae & Oean Engineering, Virginia Teh, Blaksburg, VA Abstrat This aer resents steady-state (visous) and timeaurate (invisid) numerial solutions of the flowfield inside the Virginia Teh Hyersoni Wind Tunnel (VTHST) with a Mah 4 nozzle. The numerial solutions are obtained using a omutational fluid dynamis (CFD) solver named GASP. Comarisons between the steady-state CFD solutions and available exerimental data are also resented in this aer. The first objetive of my researh is to study the steadystate flowfield harateristis of the VTHST. The seond objetive of my researh is to simulate the suersoni wind tunnel starting roess, whih has seldom been simulated using CFD. I was able to obtain reasonable Mah ontours with my steady-state CFD alulations. However, I determined that steady-state CFD alulations annot aurately redit the flowfield inside the VTHST beause muh higher ressure ratios (the total ressure in the settling hamber divided by the bak ressure at the diffuser exit) are required to start the VTHST in steady-state CFD alulations than those required to start the atual tunnel. Currently, I am running time-aurate alulations for the VTHST with a Mah 4 nozzle. Although the alulations are still in rogress, it seems that the VTHST an start at the orret ressure ratio in the time-aurate alulations. Introdution The Virginia Teh Hyersoni Wind Tunnel (VTHST) shown in Figure 1 is a unique intermittent blowdown tunnel designed and built by the Institute of Theoretial and Alied Mehanis (ITAM) in Novosibirsk, Russia. It is aable of reating Mah 2 to Mah 7 flow inside its test setion for aroximately 1.5 seonds er run. The VTHST has been used for researhes related to diret-measuring skin frition gage and Sramjet. However, the ITAM only rovided limited exerimental and alulated flowfield data to researhers at Virginia Teh. Therefore, one objetive of my researh is to use a omutational fluid dynamis (CFD) solver to alulate the harateristis of the flowfield inside the VTHST, suh as the Mah number and ressure rofiles inside the test setion to hel researhers design their exeriments. Heater Settling Chamber Nozzle Test Chamber Diffuser Silener b Q T o Notation = ressure at the diffuser exit (atmosheri) = settling hamber total ressure = onservative variable = time Gas Storage Bottles Diffuser (movable) Figure 1: The VT HST and Its Test Chamber CFD is an ideal tool to study the flowfield inside the VTHST sine it enables one to obtain the flow roerties at any osition inside the tunnel. However, sometimes it an be diffiult to get the CFD solution to onverge. Even if the solution onverges, it may not be the orret one. For examle, although I was able to obtain steady-state solutions for the VTHST with Mah 4, 6 and 7 nozzles, the ressure ratios ( o / b ) required to start the tunnel are muh higher in my steady-state CFD alulations than those required to start the real tunrrrnel. 1

2 The suersoni wind tunnel starting roess is a omlex henomenon. After the Mah number at the nozzle throat beomes 1.0, a nearly normal shokwave moves from the diverging art of the nozzle into the test hamber. Eventually, the diffuser will swallow the shok and the flow inside the test hamber ahieves the designed onditions. Sine the suersoni wind tunnel flow is inherently an unsteady roess, another way to obtain the steady-state flowfield solution is to erform time aurate alulations. Although flowfield solutions take longer to obtain using time-aurate alulations than steady-state alulations, time aurate alulation should aroximate more losely the hysis of wind tunnel flow. In addition, the results of time-aurate alulations an be used to study the suersoni wind tunnel starting roess, whih has seldom been simulated using CFD. This aer resents the results of visous steadystate CFD alulations for the VTHST with a Mah 4 nozzle, as well as some results of the invisid timeaurate alulation with the Mah 4 nozzle, whih is still in rogress Visous effets are not inluded in the time-aurate alulation beause it is believed that visous effets do not lay a signifiant role in the suersoni wind tunnel starting roess. However, in my future studies, I would like to verify this assumtion. The Mah number rofile at the nozzle exits obtained using steady-state alulation is also omared with available exerimental data. The VTHST and Grid Generation Introdution to the VTHST The VTHST is an intermittent blowdown wind tunnel. The overall length of the VTHST is 13 feet, and it features a 14X7.9X8.9in. enlosed free-jet test hamber. All arts of the VTHST are axi-symmetri exet for the test hamber. Before eah run, the eight storage bottles (11.3ft. 3 ) are filled with working gas to ressures ranging from 130 to 150atm. A time ontrol devie swithes on the main valve, and gas enters the heater, and exhausts into the room. The VTHST also features six relaeable nozzles with an exit diameter of 3.9in. designed for Mah 2.0 to 7.0 flows. The diffuser an be moved bak and forth inside the test hamber to aommodate a variety of model sizes. Grid Generation The grids for my CFD alulations are generated using Pointwise s Gridgen 15. For the visous steadystate alulations, as shown in Figure 2, the grid onsists of axi-symmetrial Mah 4 nozzle, test hamber and diffuser. The retangular test hamber is modeled as axi-symmetri to redue omutational time. This modifiation should not hange the overall flow harateristis of the tunnel signifiantly. The diffuser is inside the test hamber, and it is 200mm from the nozzle exit. Figure 3 shows the grid of the test hamber for the steady-state alulation. The grid for the entire VTHST model for the steady-state alulation has ells. Nozzle Test Chamber Diffuser Figure 2: Boundary of the Grid for Steady-state Calulation Figure 3: Test Chamber Grid for Steady-state Calulation As shown in Figure 4, for the invisid time-aurate alulation, a onial settling hamber is added in front of the axi-symmetrial Mah 4 nozzle, test hamber and diffuser assembly. The osition of the diffuser is the same as that in the steady-state alulation. The real settling hamber onsists of a onstant area dut followed by a onverging nozzle. However, sine the exat geometry of the real settling hamber is not available, a onial settling amber with aroximately the same volume is used in the CFD alulation. Figure 5 shows the grid of the test hamber for the timeaurate alulation. The grid for the entire VTHST model for the time-aurate alulation has ells. Settling Chamber Nozzle Test Chamber Figure 4: Boundary of the Grid for Time-aurate Calulation Figure 5: Test Chamber Grid for Time-aurate Calulations Flowfield Modeling Diffuser The CFD alulations are erformed using AeroSoft s GASP (General Aerodynami Simulation Program), whih solves the Reynolds Averaged Navier- Stokes Equations (RANS). GASP has been used in a wide variety of aliations suh as Sramjet 2

3 ombustors and re-entry vehile aerodynamis simulations. For my alulations, GASP was run on 8 roessors in a SGI Origin 2000 arallel omuter. In all the CFD alulations, the working gas is air, and it is assumed to be a erfet gas. Steady-state Calulation At the nozzle inlet, the Q (density, roduts of density and two omonents of veloity, and the internal energy) is fixed, but the turbulene variables are not fixed. This boundary ondition at the inlet is referred to as Fixed Q (not turbulene) in GASP. This boundary ondition requires the user to seify the ressure and Mah number at the boundary. Another boundary ondition alled P0-T0 Subsoni Inflow whih fixes the total ressure and total temerature at the nozzle inlet ould also have been used. But this boundary ondition does not work well if the geometri ontour near the boundary has large gradient suh as that shown in Figure 2. The boundary ondition at the tunnel walls are set to no-sli and adiabati. Two boundary onditions are suitable for the diffuser exit. The first one is Pbak Subsoni Outflow, whih fixes the ressure at the diffuser exit at a user-seified value. This boundary ondition an be used beause the tunnel exhausts gas into the room atmoshere, and the flow inside the tunnel deends on the bak ressure at the diffuser exit. The seond otion is to use 1 st Order Extraolation boundary ondition, whih extraolates the flow roerties at the boundary from interior ells. By not enforing a bak ressure, the flow is not fored to slow down by adverse ressure gradient, thus the tunnel should be more likely to start. I have tried both boundary onditions in my alulations. The invisid flux sheme used in my alulation is Roe, with 3 rd order satial auray and Van Albada limiter. The turbulene model used is Wilox (1998) k ω model. Gauss Seidel is used for both imliit and inner iteration shemes. Time-aurate Calulations Sine disturbanes an travel downstream of the diffuser exit before suersoni flow ours in the nozzle, using the P0-T0 Subsoni Inflow boundary ondition at the nozzle inlet should most losely aroximate the hysial situation. However, this boundary ondition will not work with the geometry used for steady-state alulations as desribed in the revious setion. So a onial settling hamber with a relatively small gradient in its ontour is added in front of the nozzle inlet as shown in Figure 4. Sine visous effets are ignored in the time-aurate alulations, the boundary ondition at the walls is set to tangeny (the veloity vetors at the walls are tangent to the wall ontour). To make the alulation as realisti as ossible, the boundary ondition at the diffuser exit is set to Pbak Subsoni Outflow before the working gas starts to exit the diffuser. Then the boundary ondition is set to 1 st Order Extraolation. As will be shown in the next setion, the tunnel will not start if the Pbak Subsoni Outflow boundary ondition is used alone. In addition, 1 st Order Extraolation annot be used alone beause the bak ressure influenes the flow roerties inside the tunnel before the flow exits the diffuser. When the gas starts to exit the diffuser, exhaust lume near the boundary ours outside of the omutational domain, and thus may alter the boundary ondition. Using 1 st Order Extraolation will enable the alulation to ontinue realistially without having to model the exhaust lume. The invisid flux sheme used in my alulation is Roe. First order satial auray is used to make the solution onverge faster and more easily. Imliit dual time steing algorithm with 2 nd order temoral auray is used to obtain the time-aurate solutions. Gauss Seidel is used for both imliit and inner iteration shemes. Results and Disussions Steady-state alulation The bak ressure is set to 94800Pa (0.93atm), the atmosheri ressure at Virginia Teh. The Fixed Q (not turbulene) boundary ondition requires the user to inut the ressure and the Mah number at the boundary. The Mah number at the nozzle inlet is set to 0.05 using the area-mah number relation for quasi-1d flow. To start the tunnel, the ressure at the inlet is set to 27atm. This ressure is well above the settling hamber total ressure of 15atm, at whih the real tunnel starts 1. Figure 5 shows the Mah ontour inside the test setion when o =15atm. Although the flow inside the nozzle ahieves Mah 4, an oblique shok stands in the test hamber, and the tunnel is not started. Figure 5: Test Chamber Mah Contour ( o 15atm = ) Figure 6 shows that the VTHST is still not started when is inreased to 20atm. However, when the o 3

4 Po is inreased to 27atm, the tunnel is started as shown in Figure 7. The streamlines in Figure 7 shows that the flowfield is uniform in the Mah 4 region of the test setion. The flow exands to Mah 6.0 after the Mah 4 region, and then slows down through an oblique shok at the diffuser inlet. Although the Mah ontour in Figure 7 looks reasonable, the ondition that rodued the flow is far from the realisti ondition. VTHST to verify the Mah number rofile at the nozzle exit Exerimental Data (Ref. 1) CFD Predition y(m) Mah# Figure 6: Test Chamber Mah Contour ( o 20atm = ) Figure 8: Mah Number Profile at the Nozzle Exit for the Steady-state Calulation T=0.0004se. T=0.001se. Figure 7: Test Chamber Mah Contour and Streamlines ( = atm ) o 27 To make the tunnel start, I also tried to set the diffuser exit boundary ondition to 1 st Order Extraolation, while leaving the nozzle inlet ondition unhanged. However, the solution diverged before it reahes steady-state, and the Mah ontour looked similar to that in Figure 5. The reason that the model tunnel annot start at the orret o may be aused by the fat that the tunnel starting roess is inherently unsteady. A steady-state alulation annot ature all the hysis in the unsteady tunnel starting roess, suh as the moving shokwave, starting vorties and the hange in boundary ondition desribed in the flowfield modeling setion. Figure 8 shows a omarison between exerimental Mah number rofile at the nozzle exit and the numerial redition. As shown in Figure 8, the exerimental and omuted Mah number rofiles outside of the boundary layer seem to agree. However, the measured boundary layer thikness is greater than that redited by CFD. This disreany ould either be due to errors in the exerimental results resented in Ref. 1, or the turbulene model used in my CFD alulation. Exeriments need to be erformed in the T=0.0018se. T=0.0028se. T=0.0038se. T=0.004se. T=0.0043se. T=0.0083se. T=0.015se. T=0.020se. T=0.0266se. Figure 9: Flow Develoment in Time Time-aurate alulation The total ressure and total temerature for the P0- T0 Subsoni Inflow boundary ondition are set to 15atm (as in a real exeriment) and 15 o C resetively. The Mah number at the settling hamber inlet is set to 4

5 0.009 using the area-mah number relation for quasi- 1D flow. The solution is saved every seonds. The flow reahes the diffuser exit at T= seonds. Thus, the boundary ondition from T=0.0001se. to T=0.0031se. is set to Pbak Subsoni Outflow. 1 st Order Extraolation boundary ondition is used after T=0.0031se. Figure 9 shows the Mah ontour inside the VTHST from T=0.0008se. to T=0.0266se. As shown in Figure 9, the flow osillates between the diverging setion of the nozzle and the front of the test hamber from T=0.0018se. to T=0.0043se. After T=0.0043se., the oblique shok starts to move toward the diffuser. At T=0.0266se., the oblique shok is swallowed by the diffuser. But if the Mah ontour at T=0.0266se. is omared to Figure 7, one an see that the tunnel is still not started omletely at T=0.0266se. Exerimental data from Ref. 1 shows that the timeaurate alulation should be run until T=0.1se. for the VTHST to ahieve steady-state flow. Currently, the time-aurate solution diverges at T=0.0266se. I am still trying to determine the ause of the divergene. One ossible ause may be that the boundary onditions are still inorret. There ould also be some subtle roblems with the grid. Figure 9 shows that, if the alulation is able to ontinue until T=0.1se., time-aurate alulations may indeed make the VTHST start at a realisti ressure ratio. Before obtaining the solution shown in Figure 9, I run the time-aurate alulation with only the Pbak Subsoni Outflow boundary ondition, and 3 rd order satial auray instead of 1 st order satial auray. The solution diverged at T=0.026se., and the Mah ontour at T=0.026se. is shown in Figure 10. From the time-aurate solution, the oblique shok seen in Figure 10 moves bak and forth between the nozzle exit and its urrent osition in Figure 10. As shown in Figure 10, if the 1 st order Extraolation boundary ondition is not used, there is little hoe that the model tunnel an start. The time-aurate alulation is erformed assuming invisid flow beause I believe that visous effets do not lay a signifiant role in wind tunnel starting roess. However, in Ref. 3, Poe states that visous effets are extremely imortant in the tunnel starting roess. Thus, visous effets will be modeled in my future studies to determine the imortane of visous effets in the suersoni wind tunnel starting roess. (a) 3 rd Order Satial Auray (b) 1 st Order Satial Auray Figure 11: Veloity Vetor Near the Nozzle Inlet at T=0.0008se. Conlusions Figure 10: Mah Contour at T=0.026se. Without using 1 st Order Extraolation Boundary Condition Another interesting henomenon assoiated with the tunnel starting roess is starting vortex, whih ours when liquid or gas is starting to move around obstales 2. Figure 11 shows that one should use 3 rd order satial auray to ature starting vorties. Visous steady-state and invisid time-aurate CFD solutions of the flowfield inside the VTHST with a Mah 4 nozzle were resented in this aer. It is found that steady-state CFD alulations annot aurately redit the flowfield inside the VTHST beause muh higher ressure ratios are required to start the VTHST in steady-state CFD alulations than those required to start the atual tunnel. Although urrently the solution for the time-aurate alulation 5

6 diverges at T=0.026se., the time-aurate alulation seems to be able to make the tunnel start at the orret ressure ratio if the alulation ould be run ast T=0.026se. It is also found that 3 rd order satial auray is needed to ature starting vorties near the nozzle inlet. Starting vorties do not our in alulations with 1 st order satial auray. Currently, I am trying to make the time-aurate alulation run ast T=0.026se. One I an get the invisid and 1 st order satially aurate alulation to reah steady-state, I will add visous effets into the omutational model to investigate the imortane of visous effets in the suersoni wind tunnel starting roess. In addition, 3 rd order satial auray will eventually be used to make my CFD simulation more realisti. Aknowledgement This researh is suorted by Virginia Sae Grant Consortium (VSGC). I would like to thank my advisor Dr. Joseh Shetz for his hel in my researh, and Dr. Reee Neel of AeroSoft In. for his hel in running GASP. Referenes 1. ITAM, Desrition and Seifiation of VT HST, Novosibirsk, Russia, Luo, X and van Dongen M. E. H., Strong Starting Vorties, htt:// 3. Poe, Alan and Goin, Kennith L., High-Seed Wing Tunnel Testing, John Wiley & Son In,