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NUMERICAL SIMULATIONS OF FLOWS PAST IXV RE-ENTRY VEHICLE AT CRAS M. Onofri 1 , R. Paciorri 1 , D. Cardillo 1 , M. Grottadaurea 1 , and A. Bonfiglioli 2 1 Centro Ricerche Aerospaziali Sapienza, Via Eudossiana 18, 00183 Roma Italy 2 Universit` a della Basilicata Dip. di Ingegneria e Fisica dell’ambiente, V.le dell’Ateneo n. 10, 85100 Potenza Italy Abstract CRAS is taking part to the ESA FLPP program contributing significantly to the computation of numer- ical simulations for to the aerothermodynamic database of the IXV vehicle. Numerical simulation of hypersonic flows represents surely a strong point for CRAS. Indeed, in this field CRAS boasts researchers with long experience and availability of state-of-art software tools. In ad- dition to this, a new computing technique which promises significantly improvements in the simulation of flows with strong shocks is presently under development at CRAS. The paper is a brief overview of the numerical techniques presently, used in the contract activities related to the IXV program or under development at CRAS together with a selection of the most significant results. 1. INTRODUCTION The researchers of CRAS (Centro Ricerche Aerospaziali Sapienza) of University of Rome have a long term experience in modeling and numerical simulation of re-entry flows. This experience originated from the participation of the University of Rome in the Hermes Project between the Eighties and Nineties and it was successively enreached and developed during the last twenty years by the participation to different national and international research programs. Thanks to this background, CRAS has joined the ESA’s FLPP project providing many numerical simulations to the aerothermodynamic database of the IXV capsule. The numerical simulation of hypersonic flows past blunt-body features several specific issues and critical problems con- cerning the physical and numerical modeling of high speed flows. For these reasons the numerical simulation of hyper- sonic flows requires often specific solvers and computing procedures. At the present, flow simulations around the IXV vehicle for the contract activities are computed by the CRAS researchers following a well-established approach based on a shock-capturing solver. Specifically, the solutions are computed by using a commercial code (Metacomps CFD++) on structured meshes whereas the numerical errors of the numerical solution are reduced by means of a specific mesh- adapting procedure applied in the shock region in order to align the mesh to the bow shock and reduce the negative effects caused by the numerical shock capture. An alternative approach is presently under development at CRAS. This new approach, which is more advanced and innovative than the previous one, is based on an unstructured hybrid solver that combines the shock-capturing and shock- fitting approaches. Indeed, the shock-fitting approach remove by root the problems related to the shock capture, since the shock is numerically modeled by a true discontinuity which is evolved by means of the Rankine-Hugoniot relations. The combination in a unique solver of the shock-capturing and shock-fitting approach allows the computation in the hybrid mode where some shocks are fitted and the remaining shocks are captured simplifying significantly from an algorithmic point of view the computation of flows with multiple shocks interacting each other. In this paper a brief description of these two computing approaches will be provided together with a selection of the most significant results obtained in the numerical simulation of flows around the IXV capsule.

Transcript of NUMERICAL SIMULATIONS OF FLOWS PAST IXV RE-ENTRY …old · NUMERICAL SIMULATIONS OF FLOWS PAST IXV...

NUMERICAL SIMULATIONS OF FLOWS PAST IXV RE-ENTRYVEHICLE AT CRAS

M. Onofri 1, R. Paciorri1, D. Cardillo1, M. Grottadaurea1, and A. Bonfiglioli2

1Centro Ricerche Aerospaziali Sapienza, Via Eudossiana 18,00183 Roma Italy2Universit̀a della Basilicata Dip. di Ingegneria e Fisica dell’ambiente, V.le dell’Ateneo n. 10, 85100 Potenza Italy

Abstract

CRAS is taking part to the ESA FLPP program contributing significantly to the computation of numer-ical simulations for to the aerothermodynamic database of the IXV vehicle.

Numerical simulation of hypersonic flows represents surelya strong point for CRAS. Indeed, in thisfield CRAS boasts researchers with long experience and availability of state-of-art software tools. In ad-dition to this, a new computing technique which promises significantly improvements in the simulation offlows with strong shocks is presently under development at CRAS.

The paper is a brief overview of the numerical techniques presently, used in the contract activitiesrelated to the IXV program or under development at CRAS together with a selection of the most significantresults.

1. INTRODUCTION

The researchers of CRAS (Centro Ricerche Aerospaziali Sapienza) of University of Rome have a long term experience inmodeling and numerical simulation of re-entry flows. This experience originated from the participation of the Universityof Rome in the Hermes Project between the Eighties and Nineties and it was successively enreached and developedduring the last twenty years by the participation to different national and international research programs. Thanks tothisbackground, CRAS has joined the ESA’s FLPP project providing many numerical simulations to the aerothermodynamicdatabase of the IXV capsule.

The numerical simulation of hypersonic flows past blunt-body features several specific issues and critical problems con-cerning the physical and numerical modeling of high speed flows. For these reasons the numerical simulation of hyper-sonic flows requires often specific solvers and computing procedures. At the present, flow simulations around the IXVvehicle for the contract activities are computed by the CRASresearchers following a well-established approach basedon a shock-capturing solver. Specifically, the solutions are computed by using a commercial code (Metacomps CFD++)on structured meshes whereas the numerical errors of the numerical solution are reduced by means of a specific mesh-adapting procedure applied in the shock region in order to align the mesh to the bow shock and reduce the negative effectscaused by the numerical shock capture.

An alternative approach is presently under development at CRAS. This new approach, which is more advanced andinnovative than the previous one, is based on an unstructured hybrid solver that combines the shock-capturing and shock-fitting approaches. Indeed, the shock-fitting approach remove by root the problems related to the shock capture, since theshock is numerically modeled by a true discontinuity which is evolved by means of the Rankine-Hugoniot relations. Thecombination in a unique solver of the shock-capturing and shock-fitting approach allows the computation in the hybridmode where some shocks are fitted and the remaining shocks arecaptured simplifying significantly from an algorithmicpoint of view the computation of flows with multiple shocks interacting each other.

In this paper a brief description of these two computing approaches will be provided together with a selection of the mostsignificant results obtained in the numerical simulation offlows around the IXV capsule.

2. NUMERICAL SIMULATIONS BASED ON SHOCK-CAPTURING APPROAC H

During the last five years, in the framework of three contracts with EADS ASTRIUM and Dassault, the CRAS researchershave computed about one hundred solutions concerning flows around the IXV re-entry vehicle in the most extreme flightconditions (M∞ = 15÷ 25). All the solutions have satisfied the quality requirementsprovided by the contracts and, then,they have been inserted in the aerothermdynamic data-base of the IXV vehicle.

As said before, all these solutions were computed by means ofthe commercial code CFD++ of Metacomp using theoverall spectrum of thermochemical and diffusion models offered by this code. Specifically, the numerical simulationswere obtained adopting several thermochemical models (theTannehill equilibrium model, the 5-species non equilibriummodels of Park and Gardner, the 11-species Park model including the ionization process and etc.), two different diffusionmodels (a model based on the Sutherland relations and the constant Smidth hypothesis and the Gupta-Yos model) andthree catalytic wall models (the fully catalytic, non-catalytic and partially-catalytic wall models)

The use of a well-tested commercial code with a wide selection of model for hypersonic flows, as CFD++, does notassure the computation of high quality solutions. In general, in a shock-capturing solution of a hypersonic flow, the shockcapture represents one of most important source of numerical error that negatively affects the quality of overall solution.For this reason specific treatments (for instance the grid-refinement and the mesh-adaption in proximity of the strongshock regions) of the computational meshes are often required in the high speed flow computations in order to reduce thenegative effects of the shock capture and to increase the solution quality. In the present case, the CRAS researchers havedeveloped a specific computing procedure based on the mesh-adaptation that assures an high solution quality. A briefdescription of the computing procedure will be illustred inthe next sections together with several examples of solutions.

2.1. Mesh generation, mesh adaption and computing procedure.

The mesh represents one of the most critical issue in the simulation of these re-entry flows. Indeed, the solution qualityandthe computational costs are strictly related to the meshes used in the computations. For this reason the CRAS researchershave developed a specific procedure for the mesh generation and mesh-adaptation. The key elements of this procedure are

• a mesh topology suitable to manage the cell clustering in thecritical regions (windward wall, bow shock and flap)

• a mesh adapting procedure for the shock regions

The computational domain around the body is split in severalblocks inside of which a structured mesh is generated. Forinstance, Figure 1 shows the block-topology around the IXV vehicle defined by the simplified aerosphape v2.2 In thiscase, the computational domain around the half capsule is split only in 10 blocks. A more complex block topology isrequired by the aeroshape v2.3 since the shape of the afterbody and flaps of the IXV vehicle is described with majordetails. In this case the computational domain is split in 28blocks (see Fig. 2). An important difference with respect tothe 10-block topology is that the some blocks are partially overlapped.

Starting from a selected block-topology a not-adapted meshis generated using a commercial mesh generator (ICEM).These meshes are characterized by a cell clustering in the proximity of the wall. Figure 2 shows some mesh details of the10-block not-adapted mesh. The overall number of cells of the computational meshes varies from 2.4 millions of cellsfor the 10-block mesh to 3.6 millions of cells for the 28-block mesh.

The numerical solutions, computed on the not-adapted meshes, are post-processed in order to adapt the mesh in the shockregions. Specifically, a mesh adapting code, developed in-house, modifies the nodes distribution along the coordinate linesnormal to the wall on the basis of the pressure gradient field clustering the mesh cells in the shock region and aligningthe cell sides to the shock. Figure 3 shows how the original mesh is modified on the base of the pressure field. The meshadapting procedure takes effect only on the blocks where strong shocks are present. Moreover, the procedure does notalter in significant way the original cell distribution inside the boundary layer. Indeed, only the mesh nodes of the shocklayer outer region and those outside the shock layer are moved toward the shocks.

Finally, the solution re-computation on the adapted mesh carries out the final solution. All examples of solutions that willbe shown in the next section were computed using this computing procedure.

Figure 1. 10-Block topology

Figure 2. 28-Block topology

2.2. Examples of simulations

As first example, we consider a sensitivity study of the catalytic wall properties by means of three simulations wheredifferent catalytic wall models are impose at the capsule walls. Specifically, the capsule geometry is defined by theaeroshape v2.2 and the flight condition of the re-entry path are reported in Table 1

Table 1. Flight conditionM∞ p∞ ρ∞ AoA δ17.7 11.51 Pa 1.7115e-04Kg/m3 45 15

Air is assumed as a gas mixture of 5 chemical species (N2,N ,O2,O,NO) in chemical non-equilibrium. The chemicalkinetics is modeled used the well-known Park model [1]. The transport properties of the gas mixture are modeled bymeans of the Gupta-Yos model [2] The viscosity and thermal conductivity of the gas mixture are calculated with theWilke’s rule, whereas the diffusion coefficient of thei species through the mixture is calculated imposing a constantSchmidt number (Sc=0.5). Three different types of catalytic wall conditions are considered:

• Fully-catalytic wall,

• Non-catalytic wall,

Figure 3. Un-adapted mesh and adapted mesh

• Partially-catalytic wall.

In a partially-catalytic wall the atom recombination process is modeled by means of recombination coefficients, alsocalled catalytic efficiencies. In the present case, the catalytic efficiency of an atomic species (γi), which is defined as theratio between the mass flux of recombining atoms and the mass flux of incident atoms is assumed to beγi = 0.04.

A qualitative comparison between the heat flux distributionover the body surface obtained by the three different numericalsolutions is shown in Fig. 4. The large differences existingbetween the prediction provided by the fully-catalytic wall andby the non-catalytic one are related to the strong chemical non-equilibrium that characterizes the flow inside the boundarylayer. In this flow conditions the wall catalycity plays an important role and the correct modeling of the surface catalycityproperties become a critical issue.

Of course, the solution obtained using the model of the partial catalytic wall described at the beginning of the this sectionprovides an estimate of the heat flux whose value is within therange defined by the non-catalytic and the fully catalyticprediction. Nevertheless the partial catalytic solution appears to be closer to the fully catalytic solution in the windwardside and to non-catalytic solution in the lateral side.

A more quantitative analysis can be performed observing figure 5, where the surface heat flux distributions along twolongitudinal planes (Y = 0, Y = 0.3) are plotted. This figure confirms the previous findings. Indeed, in the windwardregion the difference between the estimates provided by non-catalytic wall is about50% of that provided by the fullycatalytic wall. On the contrary, the differences between the partial catalytic wall and the fully catalytic wall are in generalsmall and become significant in the nose region.

The second example focuses the attention towards the comparison between the two aeroshapes (v2.2 and v2.3). Thecomparison consider two numerical simulations characterized by the same free-stream conditions (M = 25, AoA = 45, =8)and by the same model (Park 5-species model, Gupta-Yos modeland fully-catalytic wall model). The unique differencebetween the two simulations concerns the vehicle aeroshape. Figure 6 compares, the heat flux on the overall body surface

Figure 4. surface heat flux distribution: windward and lateral view

Figure 5. surface heat flux distribution along Y=0 and Y=0.3 planes

obtained on the two aeroshapes. The comparison shows some significant difference in the heat flux distributions in thenose region. Nevertheless, moving from the aeroshape v2.2 to the aeroshape v2.3, the most relevant changes caused bythe geometry can be found in the after-body and the flap regions.

Figure 6. Heat flux distribution along the surface for aeroshape v2.2 and aeroshape v2.3

Figure 7. heat flux distribution along the outside flap region

To highlight some of this differences figure 7 shows a zoom of heat flux distribution in the outer region of the flap, in thewindward side, computed on both the aeroshapes. The aeroshape v2.3 replaces the sharp corners in the flap edges withrounded surfaces (see Fig.7); this feature improves the solution along the flap edges, providing a cleaner solution withoutthe saw tooth trend featuring the aeroshape v2.2 solutions.Moreover, the new geometry removes the artificial heat fluxpeaks caused by the presence of corners in the old geometry.

3. NUMERICAL SIMULATION BASED ON SHOCK-FITTING APPROACH

The use of the mesh-adapting technique reduces the negativeeffects related to the shock capture, but these effects are notcompletely removed. For this reason for the last years the CRAS researchers together with the prof. Aldo Bonfiglioli aredeveloping a promising shock-fitting technique that works in association with a shock-capturing solver for unstructuredgrids [3].

(a) Computational mesh (b) Shock surface within the computational domain

Figure 8. Computational mesh for the IXV vehicle

The flowfield solution is computed on an unstructured background mesh composed of tetrahedra. The fitted shock frontis described using a triangulated surface that is allowed tomove, while obeying to the Rankine-Hugoniot jump relations,throughout a background tetrahedral mesh which covers the entire computational domain. At each time step, a local,constrained Delaunay tetrahedralization is applied in theneighborhood of the shock front to ensure that the triangles,which make up the shock surface, belong to the overall tetrahedral grid. The fitted shock front acts as an interior boundaryfor the unstructured shock-capturing solver, used to solvethe discretized governing equations in the smooth regions ofthe flow-field. Since the shock-fitting technique is coupled with an unstructured shock-capturing solver, shock-shockinteractions can still be dealt with by fitting one of the shocks and capturing the remaining ones.

A more detailed description of the this technique for twodimensional flows can be found in Ref.[4] whereas its extentionto three-dimensional flows is documented in Ref.[5]

3.1. Examples of simulations

To show the capabilities of this new promising technique we have considered hypersonic flow past the IXV vehicle atM∞ = 25 and45◦ angle of attack with flaps set at different deflection anglesδ1 = 15◦ andδ2 = 5◦ In all calculations,the inviscid, perfect gas model has been used, neglecting real gas and viscous effects.

A tetrahedral mesh of about 365000 points and 2169000 cells have been generated. Figure 8(a) shows the mesh used tocompute the shock-capturing solution and the shock-fittingsimulation, whereas Figure8(b) shows The triangulated shocksurface needed to the shock-fitting computation. The bow shock is fitted in the region where the shock is stronger whereasthe embedded shock originates from the flap hinge is captured. The fitted shock surface terminates before reaching theexternal boundary and it is composed of 22100 points and 43900 triangles. The test-case has been computed by meansof the shock-capturing and shock-fitting approaches on thisunstructured mesh. In addition to this, a reference solutionhas also been computed using the commercial software CFD++ [Metacomp Technologies] on a structured mesh madeof about 4 million cells locally adapted and refined in the shock region according with the precedure described in theprevious section.

Figure 9 compares the normalized pressure distribution on the body surface and within three cross-flow planes computedby means of shock-capturing and shock-fitting approaches onunstructured mesh. The comparison allows to appreciate theimprovements in shock resolution brought in by the shock-fitting calculation. The unstructured shock-capturing solution,which is characterized by a large shock thickness (compare the two solutions within the cross-flow planes 1, 2 and 3),shows visible differences with respect to the shock-fittingsolution inside the entire shock layer. These differences becomeeven more pronounced in the stagnation region.

(a) Shock-capturing solution. (b) Shock-fitting solution.

Figure 9. Normalized pressure iso-contours and floods for the IXV vehicle.

S-C Ref.

(a) Comparison between the shock-capturing so-lution and the reference one.

100 200 300 400 500 600 700 795

Ref. S-F

p/p 8

(b) Comparison between the shock-fitting solu-tion and the reference one.

Figure 10. Black solid lines and flood contours are used for the reference and fine grid solutions. Dashed and dotted linesare respectively used for the medium and coarse grid solutions.

A closer view of the stagnation region is shown in Fig. 10, which allows to draw a comparison among the variousunstructured grid solutions and the reference solution. The reference solution is compared with the, shock-capturingsolution in Fig. 10(a) and with the shock-fitting solution inFig. 10(b).

A very good agreement between the shock-fitting solution andthe reference one can be seen in Fig. 10(b). On the otherhand, significant differences exist (see Fig. 10(a)) between the reference solution and the shock-capturing one, whichpredicts a stagnation pressure value13% smaller than the reference one.

The flow-field features the presence of an embedded shock which arises in the proximity of the flap hinge and interactswith the bow shock. This flow feature gives us the chance to demonstrate the hybrid functionality of the proposed shock-fitting approach whereby the bow shock has been fitted whereasthe embedded shock has been captured.

Figure 11 compares the normalized pressure iso-contours computed within two stream-wise planes (1 and 2 in the smallframe of Fig. 11) that cut the two flaps in the middle. The comparison between the shock-capturing and the shock-fittingcalculations clearly reveals the differences; in particular, the shock-fitting solution predicts higher pressure values thanthe shock-capturing one.

Figure 11. Normalized pressure iso-contours on two sections (denoted in the top corner of the picture): shock-capturingsolution vs. hybrid solution.

p/p 8

S-F

50 100 150 200 250 300 350 400 450 500p/p∞

Ref. S-C

Figure 12. Normalized pressure iso-contours on the vehiclesurface: shock-capturing solution vs. hybrid solution.

Again, this is due to the fact that fitting the bow shock gives acleaner description of the shock layer and even thoughthe embedded shock is captured in both calculations, the better flow-field resolution upstream of the embedded shockproduces a different pressure jump and, therefore, higher pressure peaks downstream of the embedded shock.

As expected, the differences observed in the pressure distribution within the flow-field also affect the pressure distributionon the flap surface, as shown in Fig. 12. Specifically, Figure 12 compares the reference solution with the shock-capturingand shock-fitting solutions. The comparison clearly reveals the remarkable improvements that even a partial use of theshock-fitting technique can bring. Note, in particular, that the shock-fitting solution almost reproduces the reference one.

The present test case clearly shows that the proposed shock-fitting algorithm can be applied without problems to complexgeometries. Moreover, the results we have obtained show remarkable improvements upon an un-adapted shock capturingcalculation computed on a grid featuring a comparable number of grid-points and cells.

4. CONCLUSIONS

The description of computing methodologies presently usedand under developed at CRAS for the computation of hyper-sonic flows past blunt bodies and the solutions shown in the paper highlights the relevant competences and capabilitiespossessed by CRAS in this field. These competences and capabilities together with the experience acquired in the re-cent contracts concerning the IXV vehicle makes CRAS a center of national and European relevance in the numericalsimulation of re-rentry flows and a valuable asset for futureprograms.

REFERENCES

[1] Park C., 1985, AIAA paper n. 85-0247

[2] Gupta R. N. , Yos J. M. and Thompson R. A., 1990, NASA Report1232.

[3] Bonfiglioli A., 2000, International Journal of Computational Fluid Dynamics, Vol. 14, No. 1, pp. 21–39.

[4] Paciorri R. and Bonfiglioli A., 2009, Computers and Fluids, Vol. 38, No. 3, pp. 715–726.

[5] Bonfiglioli A., Grottadaurea M., Paciorri R. and SabettaF., 2010, AIAA paper n. 2010-4450

[Metacomp Technologies] Metacomp Technologies, 2010, CFD++ Homepage.