Research Interests The following text is based on an approved EPSRC proposal. The project is co-sponsored by the British Aerospace.

Numerical modelling of wind-tunnel experiments on supersonic flows of weakly ionised gases

Previous research and track record

The work proposed in this programme will be conducted by the principal investigator, Dr. Sergey Nazarenko (Warwick), co-investigators Prof. Alan Newell (Warwick) and Prof. Ron McEwen (BAe, Sowerby) and the visiting research fellow Dr. Kevin Kremeyer (Arizona).

Dr. Sergey Nazarenko is the Deputy Director of the Fluid Dynamics Research Centre (FDRC) at Warwick University and a Warwick Research Fellow at the Mathematics Institute, Warwick University. His main research interests have been concerned with theoretical and computational fluid dynamics of turbulent flows, hypersonic flows and plasmas. From 1993 to 1996, Nazarenko worked with Newell and Zakharov on solving the problem of communications blackout during hypersonic reentry by using nonlinear plasma-wave interactions [1]. This project was sponsored by the USA Air Force Office for Scientific Research (AFOSR). Since 1997, Nazarenko, Newell (Warwick) and Zakharov (Arizona) have been working on the problem of using plasmas for drag reduction on hypersonic airplanes. This project is funded by AFOSR until 2000.

Dr. Kevin Kremeyer is an experienced numerical modeller of supersonic flows. He also has some previous experience of plasma physics experiments, gained while working at Los Alamos Laboratory. Kremeyer joined the team working on using plasmas for hypersonic drag reduction in July 1997 as a postdoc at the University of Arizona under supervision of Nazarenko. Using a 2D numerical code, Kremeyer successfully modelled the shock tube experiment of Ganguly et al (Wright-Patterson AFB, USA) on shock splitting and decay in its passage through argon plasma. Starting August 1, 1998, Kremeyer will visit Warwick to work with Nazarenko, Newell and McEwen on numerical modelling of a 2D supersonic flows arising in experiments of McEwen's group.

Dr. Alan Newell is Professor of Mathematics and Chairman of the Warwick Mathematics Department. For many years, he has been a leader in the area of pattern formation and he pioneered the use of averaging methods to construct universal equations (Newell-Whitehead-Segel, complex Ginzburg-Landau, Cross-Newell, Laser Swift-Hohenberg) for the macroscopic order parameters of natural patterns which capture both their smooth and singular (defect) behaviors. He also pioneered much of the early work in solitons and was closely associated with the development of the closure equations of weak turbulence. More recently he has been heavily involved in the rapidly growing field of nonlinear optics and is co-author of a widely used text. His current interests include projects on using nonlinear properties of plasma for hypersonic flow control and to solve the re-entry blackout of communications problem, semiconductor lasers and weak turbulence theory, pattern formation on optical beams, pattern singularities and competition between nonlinearity and randomness.

Prof. Ron McEwen is the Executive Scientist at BAe, Sowerby. McEwen's team of experimentalists is cooperating in its work with other UK plasma aerodynamics groups at DERA, BAe MA\&A and MoD. The UK experimental effort is aimed at reproducing the plasma wind-tunnel experiments of Klimov et al (Moscow) and experimental study of the key physical mechanisms leading to the shock splitting and attenuation and the drag reduction [2]. The UK plasma aerodynamics group collaborate with Russian experimentalists and maintain close links with similar US teams. McEwen's experimental group is interested in collaboration with the Warwick computational team in order to gain better theoretical understanding of the plasma and fluid dynamics of the plasma wind-tunnel experiments. Kremeyer is an ideal candidate to establish such a link between the experimental and theoretical groups during his visit to the UK.

The Fluid Dynamics Research Centre at Warwick University has an established research and computing environment in both Mathematics Institute and the Engineering Department. The intention is for Dr. Kremeyer to be based at the Mathematics Institute at Warwick University in the environment of the Fluid Dynamics Research Centre (FDRC) and make frequent visits to Prof. McEwen's the Plasma Physics Group at BAe (Sowerby).

Research and its context

A. Background

The project is organized around a 7 month visit by Dr. Kevin Kremeyer to Warwick to work with Dr. Sergey Nazarenko, Prof. Alan Newell (Warwick), Prof. Ron McEwen (BAe, Sowerby) on numerical computation of the flows arising in the plasma wind-tunnel experiments. During his visit, Kremeyer will also collaborate with Drs. Cain and Gilmore (DERA, Farnborough), Dr. Evans (BAe, MA\&A) and other members of the UK plasma aerodynamics team.

Experimental and theoretical work on using plasmas to reduce drag on airplanes have recently received a new momentum in the UK, USA and other countries after the group of Klimov reported on their plasma wind tunnel experiments performed in Russia. According to Klimov et al, there was observed a significant drag reduction on a cone-nosed model when plasma was added to the supersonic gas up-stream of the model. In supersonic flows the major contribution to the drag comes from the bow shock (wave drag). Thus, the attention of Klimov et al was given to measuring the shock wave modifications after the plasma injection. It was observed that the shock decays and the shock front gets split into two jumps. The UK experimental teams coordinated by Prof. McEwen are currently working on reproducing the Russian experiments and improving the quality and reliability of the experimental techniques. Significant progress has been made on the experimental side over the past two years both in the UK, the USA and Russia [2]. However, an outstanding issue still is whether the observed shock splitting and attenuation are due largely to plasma electromagnetic effects or due solely to gas heating effects which accompany the introduction of non-equilibrium plasmas into a gas flow.

One of the research directions on the plasma-shock interaction deals with shock propagation though a discharge plasma in shock tube experiments. The shock tube geometry is simpler than the supersonic flows around cones and wedges, and the relevant gas dynamics and plasma physics is easier to study. Ganguly et al from Write-Patterson US AFB observed shock splitting and damping in a shock tube with an argon plasma section [3]. Hilburn et al have numerically modelled a shock tube experiment with a temperature inhomogeneity added to model the plasma heated region (sec. GG, Vol. 2 of Ref [2]). They showed that some features of the shock splitting effect can be observed without taking into account the non-equilibrium ionisation factor. Kremeyer reproduced the results of Hilburn et al and studied the shock structure in greater detail [4]. Together with Nazarenko and Newell, Kremeyer showed that the shock splits into two jumps: the front one is a shock and the back is a contact discontinuity. It was further shown that the region between the two jumps is filled with vorticity generated by the shock passing through the density gradient. This flow significantly affects the shock dynamics and has a complicated 2D structure. It consists of two major regions, one of which is a quasi-stationary shock-jet system (front) and another is an unstable recirculating region (back).

Thus, shock propagation in nonumiformly heated gases is an applied mathematical problem having both a deep fluid dynamics content and an imporatance for industrial applications. Doing the shock-tube numerical experiments, Dr. Kremeyer gained the experience necessary for computing flows having a more complicated geometry corresponding to the wind tunnel experiments of Prof. McEwen's plasma group.

B. Programme and Methodology

In the first instance, a series of numerical CFD experiments will be performed by Dr. Kremeyer, where the plasma heating effect (but not ionisation) is added to a supersonic 2D wedge flow to see whether splitting of the nose shock is simulated. The 2D wedge flow has similar shock system as the flow around a cone, but it is easier to compute. Thus, computing the wedge flows one can understand the structure of the flows round cone-nosed models used in experiments of McEwen and his Plasma aerodynamics group. The goal of such numerical experiments is to answer the question whether the observed shock splitting and damping are solely due the gas heating accompanying the plasma generation or it is due to electromagnetic effects associated with non-equilibrium plasmas.

Dr. Kremeyer's experience with numerical modelling of the shock tube flow is going to be very helpful at this stage of work. To simulate the shock tube geometry, Kremeyer considered a 100:1 rectangular domain with "reflecting slip" boundary conditions on the walls and fixed pressure, density and zero velocity at the ends of the tube. The numerical method used to calculate the 2D compressible Euler equations is based on a 5th order weighted ENO scheme to find the flux eigenvectors at half gridpoints and a 3rd order Runge-Kutta routine to propagate the half gridpoint fluxes and find the new fluid parameters at the real gridpoints. The wedge geometry brings about many new factors compared to the shock tube problem, such as the bow shock, the flow obliqueness, possible shock-surface interaction. As in the shock tube problem, the penetration of an externally heated flow through the shock will be accompanied by vorticity generation via the baroclinic mechanism. However, such a vortical flow is going to possess a unique and non-obvious structure due to the oblique shock structure and interaction with boundaries associated with the wedge geometry. It is important that Kremeyer's code is computing nonstationary flow because the vortical flows which arise are usually very unstable and non-stationary. Numerical modelling of the wedge flow will have to be done at a higher resolution than in the shock tube simulation. It involves certain challenges such as, for example, finding a good and informative way of visualization and interpretation of massive amounts of numerical data. Good care will have to be taken to ensure the code stability and convergence. Lengthy visits will be made by Dr. Kremeyer to the Plasma Physics Group at BAe (Sowerby) and to the Hypersonics Group at DERA (Farnborough) to collaborate with experimentalists. This collaboration will enable Dr. Kremeyer and Dr. Nazarenko to tune their computational and theoretical programme to the experimental realities. In addition to gaining a better understanding of the current experimental results, this may help better planning of future experiments. The experimental groups at BAe and DERA are familiar with the preliminary shock tube computations of Kremeyer et al and they are very interested in a close collaboration with the Warwick-Arizona theoretical team and, in particular, in the UK visit of Dr. Kremeyer. A clear sign of this interest is the fact that a partial funding of Dr. Kremeyer's visit was approved at BAe by Mr. T.J. Hatch, the Chief Engineer responsible for this area of work at BAe MA&A.

We expect that Dr. Kremeyer will need from four to five months to obtain reliable numerical results on the structure of the wedge flow with external gas heating and thereby answer the question whether the effect of plasma on shock dynamics is purely thermal and not electromagnetic. In the case of positive answer to this question, the rest of Dr. Kremeyer's visit will be devoted to numerical study of robustness of the computational results with respect to the variations in the geometrical shape and various means of plasma generation. We expect that there will be substantial feedback from experimentalists in the form of requests for numerical modelling of different experimental setups. It is the main goal in this project to work in close contact with experimentalists whose permanent feedback will enable to adjust the direction of the numerical modelling of Dr. Kremeyer.

It is possible, however, that there will be no satisfactory agreement between the numerical simulations ignoring the electromagnetic effects and experimental data. In this case, Dr. Kremeyer will spend the second part of his visit on including the non-equilibrium plasma processes into his numerical model. Plasma processes are very sensitive to the particular choice of the plasma parameters, such as the concentration, electron and ion temperatures, collision and plasma frequencies, Debye radius, etc. Because of the great variety and complexity of the plasma processes, one has to develop a simplified model which takes into account only the most important processes. Close work with experimentalists will be absolutely crucial at this stage to identify the relevant range of the plasma parameters and to single out the most important of the plasma processes to be included into the numerical model. Dr. Kremeyer's previous experience with plasma experiment at the Los Alamos laboratory will be very helpful for this part of the project. Dr. Kremeyer will closely collaborate with Dr. Nazarenko who has a plasma experience from a two-year work at the Kurchatov Institute for Atomic Physics, four years at Radio-Technical Institute in Moscow and tree-year work on the communications blackout problem at the University of Arizona.

C. Relevance to beneficiaries

The principal beneficiaries of this work will be the UK and international experimental and theoretical groups studying the possibility to reduce drag on airplanes using weakly ionized gases. Dr. Kremeyer's work during his visit to the UK will help to establish steady links and enhance the collaboration between the theoretical group at Warwick and experimental plasma groups at BAe and DERA. In perspective, a positive solution of the drag reduction problem would have an immediate impact on the aircraft technology. Members of the Fluid Dynamics Research Centre at Warwick, from both Mathematics Institute and the Engineering Department, will also benefit from Dr. Kremeyer's expertise in computational fluid dynamics.

D. Dissemination and Exploitation

The results of this work will be published in the usual refereed academic journals and reported at the plasma aerodynamics conferences.


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