Two active flow control methods are investigated numerically to understand the mechanism by which they control aerodynamics in the presence of severe flow separation on an airfoil. In particular, synthetic jets are applied to separated flows generated by additional surface feature (the actuators) near the trailing edge to obtain Coanda-like effects, and an impulse jet is used to control a stalled flow over an airfoil. A moving-grid scheme is developed, verified and validated to support simulations of external flow over moving bodies. Turbulent flow is modeled using detached eddy simulation (DES) turbulence models in the CFD code CDP (34) developed by Lopez (54). Synthetic jet actuation enhances turbulent mixing in flow separation regions, reduces the size of the separation, deflects stream lines closer to the surface and changes pressure distributions on the surface, all of which lead to bi-directional changes in the aerodynamic lift and moment. The external flow responds to actuation within about one convective time, which is significantly faster than for conventional control surfaces. Simulation of pitching airfoils shows that high-frequency synthetic jet affects the flow independently of the baseline frequencies associated with vortex shedding and airfoil dynamics. These unique features of synthetic jets are studied on a dynamically maneuvering airfoil with a closed-loop control system, which represents the response of the airfoil in wind-tunnel experiments and examines the controller for a rapidly maneuvering free-flight airfoil. An impulse jet, which is applied upstream of a nominal flow separation point, generates vortices that convect downstream, interact with the separating shear layer, dismantle the layer and allow following vortices to propagate along the surface in the separation region. These following vortices delay the separation point reattaching the boundary layer, which returns slowly to its initial stall condition, as observed in wind-tunnel experiments. A simple model of the impulse jet actuator used herein is found to be sufficient to represent the global effects of the jet on the stalled flow because it correctly represents the momentum injected into the flow. / text

Analysis of unsteady flows is a very challenging topic of research. A decade ago, potential flow equations were used to predict unsteady pressures on oscillating bodies. Recognising the fact that nonlinear aerodynamics is essential to analyse unsteady flows accurately, particularly in transonic and supersonic flows, different Euler formulations operating on moving grids have emerged recently as important CFD tools for unsteady aerodynamics. Numerical solution of Euler equations on moving grids based on upwind schemes such as the ones due to van Leer and Roe have been developed for the purpose of numerical simulation of unsteady transonic and supersonic flows. In the present work, Euler computations based on yet another recent robust upwind scheme (for steady flows) namely Kinetic Flux Vector Splitting (KFVS) scheme due to Deshpande and Mandal is chosen for further development of a time accurate Euler solver to operate on problems involving moving boundaries. The development of an Euler code based on this scheme is likely to be highly useful to analyse problems of unsteady aerodynamics and computational aeroelasiticity especially when it is noted that KFVS has been found to be an extremely robust scheme for computation of subsonic, transonic, supersonic and hypersonic flows. The KFVS scheme, basically exploits the connection between the linear scalar Boltzmann equation of kinetic theory of gases and the nonlinear vector conservation law, that is, Euler equations of fluid dynamics through moment method strategy. The KFVS scheme has inherent simplicity in splitting the flux even on moving grids due to underlying particle model. The inherent simplicity of KFVS for moving grid problems is due to its relationship with the Boltzmann equation. If a surface is moving with velocity w and a particle has velocity v, then it is quite reasonable to do the splitting based on (v-w)<0 or >0. Only particles having velocity v greater than w will cross the moving surface from left to right and similar arguments hold good for particles moving in opposite direction. It is therefore quite natural to extend KFVS by splitting the Maxwellian velocity distribution at Boltzmann level based on the sign of the normal component of the relative velocity. The relative velocity is the difference between the molecular velocity (v) and the velocity of the moving surface(w). This inherent simplicity of the Kinetic Flux Vector Splitting scheme on Moving Grids (KFMG) method has prompted us to extend the same ideas to 2-D and 3-D problems leading to the present KFMG method. If w is set to zero then KFMG formulation reduces to the one corresponding to KFVS. Thus KFMG formulations axe generalisation of the KFVS formulation. In 2-D and 3-D cases, in addition to the KFMG formulation, the method to move the grids, the appropriate boundary conditions for treating moving surfaces and techniques to improve accuracy in space and time are required to be developed. The 2-D and 3-D formulations based on Kinetic Flux Vector Splitting scheme on Moving Grids method have been developed for computing unsteady flows. Between two successive time steps, the body changes its orientation in case of an oscillation or it deforms when subjected to, aerodynamic loads. In either of these cases the grid corresponding to the first time step has to be moved or regenerated around the displaced or deformed body. There are several approaches available to generate grids around moving bodies. In the present work, the 'spring analogy method' is followed to obtain grid around deflected geometries within the frame work of structured grid. Using this method, the grids are moved from previous time to the current time. This method is capable of tackling any kind of aeroelastic deformation of the body. For oscillating bodies, a suitable boundary condition enforcing the flow tangency on the body needs to be developed. As a first attempt, the body surface has been treated as an 1-D piston undergoing compression and expansion. Then, a more general Kinetic Moving Boundary Condition(KMBC) has been developed. The KMBC uses specular reflection model of kinetic theory of gases. In order to treat fixed outer boundary, Kinetic Outer Boundary Condition(KOBC) has been applied. The KOBC is more general in the sense that, it can treat different type of boundaries (subsonic, supersonic, inflow or out flow boundary). A 2-D cell-centered finite volume KFMG Euler code to operate on structured grid has been developed. The time accuracy is achieved by incorporating a fourth order Runge-Kutta time marching method. The space accuracy has been enhanced by using high resolution scheme as well as second order scheme using the method of reconstruction of fluxes. First, the KFMG Euler code has been applied to standard test cases for computing steady flows around NACA 0012 and NACA 64AQ06 airfoils in transonic flow. For these two airfoils both computational and experimental results are available in literature. It is thus possible to verify (that is, prove the claim that code is indeed solving the partial differential equations + boundary conditions posed to the code) and validate(that is, comparison with experimental results) the 2-D KFMG Euler code. Having verified and validated the 2-D KFMG Euler code for the standard test cases, the code is then applied to predict unsteady flows around sinusoidally oscillating NACA 0012 and NACA 64A006 airfoils in transonic flow. The computational and experimental unsteady results are available in literature for these airfoils for verification and validation of the present results. The unsteady lift and normal force coefficients have been predicted fairly accurately by all the CFD codes. However there is some difficulty about accurate prediction of unsteady pitching moment coefficient. Even Navier-Stokes code could not predict pitching moment accurately. This issue needs further in depth study and probably intensive computation which have not been undertaken in the present study. Next, a two degrees of £reedom(2-DOF) structural dynamics model of an airfoil undergoing pitch and plunge motions has been coupled with the 2-D KFMG Euler code for numerical simulation of aeroelastic problems. This aeroelastic analysis code is applied to NACA 64A006 airfoil undergoing pitch and plunge motions in transonic flow to obtain aeroelastic response characteristics for a set of structural parameters. For this test case also computed results are available in literature for verification. The response characteristics obtained have showed three modes namely stable, neutrally stable and unstable modes of oscillations. It is interesting to compare the value of airfoil-to-air mass ratio (Formula) obtained by us for neutrally stable condition with similar values obtained by others and some differences between them are worth mentioning here. The values of \i for neutral stability are different for different authors. The differences in values of (Formula) predicted by various authors are primarily due to differences which can be due to grid as well as mathematical model used. For example, the Euler calculations, TSP calculations and full potential calculations always show differences in shock location for the same flow problem. Changes in shock location will cause change in pressure distribution on airfoil which in turn will cause changes in values of \L for conditions of neutral stability. The flutter speed parameter(U*) has also been plotted with free stream Mach number for two different values of airfoil - to - air mass ratio. These curves shown a dip when the free stream Mach number is close to 0.855. This is referred as "Transonic Dip Phenomenon". The shock waves play a dominant role in the mechanism of transonic dip phenomenon. Lastly, cell-centered finite volume KFMG 3-D Euler code has been developed to operate on structured grids. The time accuracy is achieved by incorporating a fourth order Runge-Kutta method. The space accuracy has been enhanced by using high resolution scheme. This code has 3-D grid movement module which is based on spring analogy method. The KMBC to treat oscillating 3-D configuration and KOBC for treating 3-D outer boundary have also been formulated and implemented in the code. The 3-D KFMG Euler code has been first verified and validated for 3-D steady flows around standard shapes such as, transonic flow past a hemisphere cylinder and ONERA M6 wing. This code has also been used for predicting hypersonic flow past blunt cone-eylinder-flare configuration for which experimental data are available. Also, for this case, the results are compared with a similar Euler code. Then the KFMG Euler code has been used for predicting steady flow around ogive-cylinder-ogive configuration with elliptical cross section. The aerodynamic coefficients obtained have been compared with those of another Euler code. Thus, the 3-D KFMG Euler code has been verified and validated extensively for steady flow problems. Finally, the 3-D KFMG based Euler code has been applied to an oscillating ogive-cylinder-ogive configuration in transonic flow. This test case has been chosen as it resembles the core body of a flight vehicle configuration of interest to DRDO,India. For this test case, the unsteady lift coefficients are available in literature for verifying the present results. Two grid sizes are used to perform the unsteady calculations using the present KFMG 3-D Euler code. The hysteresis loops of lift and moment coefficients confirmed the unsteady behaviour during the oscillation of the configuration. This has proved that, the 3-D formulations are capable of predicting the unsteady flows satisfactorily. The unsteady results obtained for a grid with size of 45x41x51 which is very close to the grid size chosen in the reference(Nixon et al.) are considered for comparison. It has been mentioned in the reference that, a phase lag of (Formula) was observed in lift coefficients with respect to motion of the configuration for a free stream Mach number of 0.3 with other conditions remaining the same. The unsteady lift coefficients obtained using KFMG code as well as those available in literature are plotted for the same flow conditions. Approximately the same phase lag of (Formula) is present (for (Formula)) between the lift coefficient curves of KFMG and due to Nixon et al. The phase lag corrected plot of lift coefficient obtained by Nixon et al. is compared with the lift coefficient versus time obtained by 3-D KFMG Euler code. The two results compare well except that the peaks are over predicted by KFMG code. It is nut clear at this stage whether our results should at all match with those due to Nixon et al. Further in depth study is obviously required to settle the issue. Thus the Kinetic Flux Vector Splitting on Moving Grids has been found to be a very good and a sound method for splitting fluxes and is a generalisation of earlier KFVS on fixed grids. It has been found to be very successful in numerical simulation of unsteady aerodynamics and computational aeroelasticity.

The results from computer simulations of the gas-dynamic processes that occur during and after the rupture of diaphragms within shock tubes and expansion tubes are presented. A two-dimensional and axisymmetric finite-volume code that solves the unsteady Euler equations for inviscid compressible flow, was used to perform the simulations. The flow domains were represented as unstructured meshes of triangular cells and solution-adaptive remeshing was used to focus computational effort in regions where the flow-field gradients were high. The ability of the code to produce accurate solutions to the Euler equations was verified by examining the following test cases: supersonic vortex flow between two arcs, an ideal shock tube, and supersonic flow over a cone. The ideal shock tube problem was studied in detail, in particular the shock speed. The computed shock speed was accurate when the initial pressure ratio was low. When the initial pressure ratio was high the ow was dificult to resolve because of the large density ratio at the contact surface where significant numerical diffusion occurred. However, solution- adaptive remeshing was used to control the error and reasonable estimates for the shock speed were obtained. The code was used to perform multi-dimensional simulations of the gradual opening of a primary diaphragm within a shock tube. The development of the flow, in particular the contact surface was examined and found to be strongly dependent on the initial pressure ratio across the diaphragm. For high initial pressure ratios across the diaphragm, previous experiments have shown that the measured shock speed can exceed the shock speed predicted by one- dimensional models. The shock speeds computed via the present multi-dimensional simulation were higher than those estimated by previous one-dimensional models and were closer to the experimental measurements. This indicates that multi- dimensional ow effects were partly responsible for the relatively high shock speeds measured in the experiments. The code also has the ability to simulate two-dimensional fluid-structure interac- tions. To achieve this the Euler equations are solved for a general moving frame of reference. Mesh management during a simulation is important. This includes the ability to automatically generate a new mesh when the current mesh becomes distorted (due to the motion of the structures) and the transfer of the solution from the old mesh to the new. The shock induced rupture of thin diaphragms was examined. Previous one dimen- sional models are awed because they do not simultaneously consider the diaphragm mass and allow the upstream gas to penetrate the diaphragm mass. Two multi- dimensional models which allow the upstream gas to penetrate are described. The first model assumes the diaphragm vaporises immediately after the arrival of the incident shock. The second model assumes the diaphragm shatters into a number of pieces which can be treated as rigid bodies. The results from both models are compared with experimental data.

A set of algorithms building a program package for the generation of twoandthree-dimensional unstructured/hybrid grids around complex geometrieshas been developed. The unstructured part of the grid generator is based on the advancing frontalgorithm. Tetrahedra of variable size, as well as directionally stretched tetrahedracan be generated by specification of a proper background grid, initiallygenerated by a Delaunay algorithm. A marching layer prismatic grid generation algorithm has been developedfor the generation of grids for viscous flows. The algorithm is able to handleregions of narrow gaps, as well as concave regions. The body surface is describedby a triangular unstructured surface grid. The subsequent grid layers in theprismatic grid are marched away from the body by an algebraic procedurecombined with an optimization procedure, resulting in a semi-structured gridof prismatic cells. Adaptive computations using remeshing have been done with use of a gradientsensor. Several key-variables can be monitored simultaneously. The sensorindicates that only the key-variables with the largest gradients give a substantialcontribution to the sensor. The sensor gives directionally stretched grids. An algorithm for the surface definition of curved surfaces using a biharmonicequation has been developed. This representation of the surface canbe used both for projection of the new surface nodes in h-refinement, and theinitial generation of the surface grid. For unsteady flows an algorithm has been developed for the deformationof hybrid grids, based on the solution of the biharmonic equation for the deformationfield. The main advantage of the grid deformation algorithm is that itcan handle large deformations. It also produces a smooth deformation distributionfor cells which are very skewed or stretched. This is necessary in orderto handle the very thin cells in the prismatic layers. The algorithms have been applied to complex three-dimensional geometries,and the influence of the grid quality on the accuracy for a finite volumeflow solver has been studied for some simpler generic geometries. / QC 20100812