**Principal Investigator**
Frank P Houwing **Project **n13

Department of Physics and Theoretical Physics, **Machine
**VP

Faculty of Science

**Co-Investigators** Russell
R Boyce, John Sandeman,

Department of Physics and Theoretical Physics, Faculty
of Science and Department of Aerospace and Mechanical Engineering,
Australian Defence Force Academy

**Non-equilibrium Re-entry Flows (CFD Validation)**

In recent times, international research into the development of the next generation aerospace vehicles has focussed on the design of the so called "Space Planes". These vehicles will be reuseable spacecrafts, which are significantly more advanced than the current Space Shuttle. Their flight paths will range from suborbital to orbital, and, while their main functions will be to launch and service satellites, they can also be used for international travel. As a prospective means of futuristic travel, the Space Plane will be capable of significantly reducing intercontinental flight times.

One of the problems facing the design engineer is the fact that, for the proposed flight paths and speeds, the phenomenon of "real gas behaviour" becomes important. This phenomenon is a result of the shock wave produced at the nose of the vehicle when travelling at supersonic speeds. (In fact, because the flight speeds of these vehicles are so high, the term "hypersonic" rather than "supersonic" is used.) This shock wave elevates the temperature of the air through which the vehicle is travelling, causing a whole range of gas phase chemical processes to occur, in particular:the excitation of molecular modes of vibration; the dissociation of oxygen and nitrogen into their atomic forms; the formation of other chemical species through recombination reactions; and the ionisation of both molecular and atomic species. These "real gas effects" play an important role in the thermodynamics of the air flow around the vehicle. For example, they can influence the pressure distribution on control surfaces, and the heat loading to the thermal shields. These consequences therefore affect the flight performance, as well as the choice of thermally protective surface materials. Understanding the role of these real gas effects requires a combination of theoretical, numerical and experimental work. The research program carried out at ANU forms part of this integrated approach with numerical work being performed on the university's supercomputer, and the experimental work undertaken on the university's hypersonic wind tunnel, the T3 Shock Tunnel.

As with all wind tunnels, however, the ANU shock tunnel facility can simulate only partly the free flight behaviour. It is therefore vitally important to translate the wind tunnel data to the free flight regime. One of the most efficient ways of achieving this is to test the computational fluid dynamic (CFD) codes which are currently under development by using them to simulate the experimental flows. Once the codes can reproduce these model flows reliably, there can be reasonable confidence that they may then be used to predict the free flight behaviour. This requires firstly obtaining as much data as possible from each wind tunnel run, and secondly running and developing the codes with the experimental input data to test their simulation proficiency. Naturally, this is best accomplished on a local machine where the whole program can be integrated.

Deutsche Aerospace (DASA) of Germany have been developing a family of coupled Euler/boundary layer CFD codes on a Fujitsu VP2200. These codes calculate hypersonic flows over blunt bodies, including the effects of nonequilibrium chemical reactions, and DASA have supplied them to the ANU as part of a collaborative research venture. The aim of the project is to attempt to validate those codes by means of comparison of their predictions with experimental data produced by the ANU shock tunnel.

**What are the basic questions addressed?**

The important issues, which this research project seeks to explore, are as follows:

(i) Determine which measureable flow parameters (e.g., bow shock standoff distance, wall heat transfer, shock layer temperatures and chemical species concentrations) provide the most critical check of the CFD code.

(ii) Examine the physics, chemistry and numerical algorithms incorporated in the code to determine their acuracy and suitability to successfully predict the experimental measurements.

(iii) Where disagreement between numerical simulation and experiment exist, determine whether the discrepancies arise from numerical inaccuracies in the code, or in bad assumptions or incorrect physics and chemistry incorporated. In exploring explanations for the existence of dicrepancies, particular attention will be devoted to determine whether: disagreements arise from peculiarities associated with the experiments that are not accounted for by the code; or whether they arise from an insufficient knowledge of the nature of the free stream flow produced.

(iv) With the range of flow conditions and measurements possible with the available experimental facilities, and with the results of the subsequent CFD/experiment comparisons, determine over what part of the flight domain can the code be said to be validated and hence confidently applied.

**What are the results to date and future of the
work?**

On the experimental side of the work, the hypersonic flow over a hyperboloid body has been investigated for a number of test conditions, designed to simulate "ideal gas" and "real gas" behaviour. The "real gas" conditions consisted of two subsets, one wherein chemical equilibrium assumptions were valid, the other wherein nonequilibrium relaxation processes were important. In addition, two flow geometries were adopted. In the first geometry, the body's axis of symmetry was aligned with the principle direction of the flow produced by the shock tunnel. In the second geometry, this axis was oriented at a 15 degree angle to this flow direction.

A number of different flow diagnostics were used in studying these flows. These are described briefly below (not necessarily in chronological order).

Firstly, line-of-sight interferometry was performed using a Mach Zehnder interferometer and a pulsed light source. This interferometry allowed projections of the shock shape and projections of the integrated refractive index to be produced on a plane at right angles to the line-of-sight. Secondly, the distribution of heat transfer rates on the model surface was measured using coaxial thermocouples. Thirdly, the distribution of the static pressure on the body was measured using piezoelectic and piezoresistive transducers. Fourthly, coherent anti-Stokes Raman scattering (CARS) was used to measure the rotational and vibrational temperatures in the freestream flow and also in the shock layer.

The above experimental work was augmented by investigations of flows over cylinders and wedges, for which the flow diagnostics included laser-induced predissociation fluorescence (LIPF) and planar laser-induced fluorescence (PLIF). Some of this work was carried out in collaboration with the High Temperature Gasdynamics Laboratory (HTGL) at Stanford University.

For all of the above mentioned experiments, comparative numerical work was undertaken. In this numerical work, a number of different CFD codes were employed: (i) a two-dimensional (axisymmetric) ideal gas code; (ii) a three-dimensional ideal gas code; (iii) a two-dimensional equilibrium real gas code; (iv) a three-dimensional equilibrium real gas code; (v) a two-dimensional non-equilibrium real gas code; (vi) a three-dimensional non-equilibrium real gas code.

Various philosophies are adopted to experimentally validate CFD codes. However, an approach that is proving to be extremely useful is one that compares results obtained via optical techniques with computer generated flow images. The production of these images has been termed Computational Flow Imaging (CFI) by various authors. In essence it is the art and science of generating digital images of theoretical fluid dynamic phenomena in formats that mimic optical observations of real flow fields. These optical observations could be shadowgraph, schlieren, interferometric or spectroscopic images. Models for the flow measurement processes must therefore be superimposed on the models used to predict the flow behaviour.

In previous experiments involving two-dimensional hypervelocity nitrogen flows over cylinders, it has been possible to make direct comparisons between the interferometrically-measured and CFD-predicted density fields. This is because the interferometrically-produced phase data is the result of the integration of the refractive index [and hence the species densities via the Gladstone-Dale relation for a multi-component gas ] along the line-of-sight. For a two dimensional flow, the flow parameters are constant along that line-of-sight, and so phase contours in the interferograms correspond directly to refractive index contours in the flowfield. This makes it possible to compare fringe centres in an interferogram with CFD-generated isopycnals. For complex three dimensional flows, however, such direct comparisons are not possible due to the varying flow conditions along the line-of-sight. Instead, the reliability of the code in being able to predict the correct density field needs to be tested indirectly.

As part of this CFD-validation project, CFI has been used to predict the phase distribution measured interferometrically as a function of viewing angle for the three dimensional flow about the hyperboloid described above. This is achieved by using CFI to determine theoretical phase maps by performing numerical line-of-sight integration of the density data produced by the CFD code. These phase maps can then be compared with those produced by interferometry experiments. This method has certain short-comings though, since a range of different total and species density distributions can produce identical phase maps, which introduces a certain degree of ambiguity into the CFD validation process. In an attempt to remove this ambiguity, CFI-generated phase maps for seven different viewing angles of the same flow are produced and compared with interferometric phase measurements for these viewing angles.

The CFI technique was also used for the purpose of validating the CFD codes through PLIF imaging of the flows over the cylinders and wedges. However, in the case of the PLIF-CFI work, line of sight integration was unnecessary, because the PLIF method allows three-dimensional imaging of a planar cross-section of the flow.

In addition to the CFI method, direct comparisons were made between the numerically-predicted and experimentally-measured flow temperatures. In particular, the theoretical temperatures were compared with temperatures measured via the CARS, LIPF and PLIF techniques.

The CFD codes were also used to predict the heat transfer and static pressure distributions over the body surface, and these were compared with the experimentally-measured values.

The future of the work lies with extending the CFI method to produce theoretical PLIF images for high enthalpy flow conditions, for which the following considerations are important. PLIF is an optical method for measuring spatial distributions of species concentration, temperature, and velocity in reactive environments. In most practical environments PLIF images are complicated by the effects of collisional de-excitation, or quenching, of laser-excited molecules. Because collisional quenching depends on several unknown and hard-to-measure variables, such as the composition of the collisional environment, quenching severely limits the ability to determine spatial species distributions from PLIF images. The temperature-dependent quenching cross-sections have been measured for many of the collision partners of interest, however, further data is required for quenching by vibrationally-excited species and metallic contaminants. Hence the first aim of future work is to measure the temperature-dependent quenching cross-section of the vibrationally-excited molecules and the metallic contaminants. The second aim of future work is to develop a theoretical model to produce computer-generated PLIF images for real-gas (chemically reacting) environments where collisional quenching of the fluorescence is important. The existing CFD codes for hypervelocity non-equilibrium air flows will be used for the calculation of the flowfield, producing spatial distributions of temperature, pressure, species density and velocity. A small-perturbation model for the PLIF intensity will be used to account for collisional quenching by the various components of the reacting gas, including vibrationally-excited molecules and metallic impurities that are present in many impulse-flow facilities. The purpose of generating the theoretical PLIF images is to validate CFD codes through direct comparison of theoretically-predicted fluorescence intensities with intensities measured from single-line PLIF images.

**What computational techniques are used and why
is a supercomputer required?**

The complete calculation of a flow field involves solving the three-dimensional Navier-Stokes equations. However, this requires far too much CPU time and memory. The codes use a much cheaper but quite accurate method, in which the flow field is divided into its viscous part (the boundary layer on the body) and its inviscid part (the region between the boundary layer and the shock). The Euler equations (the inviscid form of the N-S equations) are solved in the inviscid region using a split-matrix algorithm with Runge-Kutta time stepping, starting from an initial guess for the shock shape and inviscid flow field and using a bow-shock fitting approach. The second-order boundary layer equations (the viscous high Reynolds number second-order approximation to the N-S equations) are solved in the boundary layer using a finite-difference space-marching method. Both calculations are iteratively coupled together, the output of one used as the input for the other. Good results are obtained with only one iteration. Different versions of the code compute 2D/axisymmetric or 3D flowfields, for perfect gas, equilibrium chemistry or nonequilibrium chemistry.

The complexity of the flow fields, especially those exhibiting non-equilibrium chemical effects, and the mathematical nature of the governing equations means that enormous computing speed and memory are required in order to obtain accurate and economically viable (for the code's use as an engineering tool) results. For example, it is estimated that a converged inviscid solution for the 3-d nonequilibrium air code would take approximately 4 months of CPU time if run on the local Sun 4/280.

**Publications**

*Multiple Interferometric Views of Hypervelocity
Air Flows for Computational Fluid Dynamics Validation*
Journal of Spacecraft and Rockets, (submitted). R. R. Boyce,
J. W. Morton, A. F. P. Houwing and C. Mundt,

*Rotational and Vibrational Temperature Measurements
using CARS in a Hypervelocity Shock Layer Flow and Comparisons
with CFD calculations* , R. R. Boyce, D.
R. N. Pulford, A. F. P. Houwing and C. Mundt, Shock Waves Journal,
in press.

*Computational Fluid Dynamics Validation using
Multiple Interferometric Views of a Hypersonic Flowfield,*
R. R. Boyce, J. W. Morton, A. F. P. Houwing, C. Mundt and D. J.
Bone, Journal of Spacecraft and Rockets, in press.

*PLIF Thermometry in a High Temperature Shock Layer
Flow on a Cylinder in a Supersonic Jet,*
A. F. P. Houwing, J. L. Palmer, R. R. Boyce, M. C. Thurber, S.
D. Wehe and R. K. Hanson, AIAA 95-0515, (1995).

*Flow Imaging and Comparisons for Three Dimensional
Shock Layer Flows over a Blunt Body* R.
R. Boyce, J. W. Morton, A. F. P. Houwing and C. Mundt, Computational,
in Second Pacific International Conference on Aerospace Science
& Technology; B. Belton; D. Long; C. Martin; M. Scott; M.
Weller and L. Wood, Ed.; [The Institution of Engineers, Canberra,
Australia], pp. 419-426 (1995).

*Comparison of CFD with CARS Measurements in Hypervelocity
Nitrogen Flows,* R. R. Boyce, D. R. N.
Pulford, A. F. P. Houwing, C. Mundt and R. J. Sandeman, Shock
Waves @ Marseilles: 19th International Symposium on Shock Waves;
R. Brun and L. Z. Dumitrescu, Ed.; [Springer-Verlag, Heidelberg,
Germany], pp. 27-32 (1995).