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A three-dimensional instability that predicts subcritical transition in plane channel flows in good agreement with experiment is discussed. Both full simulations of the Navier-Stokes equations and a three-dimensional linear analysis about two-dimensional finite amplitude states confirm that two-dimensional secondary flows are strongly unstable to small three-dimensional perturbations.
The NACA 0012 profile at Mach 0.5 was investigated in a wind tunnel with adaptive walls. It is found that adaptation of the flexible walls is possible in the high angle of attack range on both sides of maximum lift. Oil film photographs of the flow at the profile surface show three dimensional effects in the region of the corners between the profile and the sidewall. It is concluded that pure two dimensional separated flow is not possible.
Computational predictions of turbulent flow in sharply curved 180 degree turn around ducts are presented. The CNS2D computer code is used to solve the equations of motion for two-dimensional incompressible flows transformed to a nonorthogonal body-fitted coordinate system. This procedure incorporates the pressure velocity correction algorithm SIMPLE-C to iteratively solve a discretized form of the transformed equations. A multiple scale turbulence model based on simplified spectral partitioning is employed to obtain closure. Flow field predictions utilizing the multiple scale model are compared to features predicted by the traditional single scale k-epsilon model. Tuning parameter sensitivities of the multiple scale model applied to turn around duct flows are also determined. In addition, a wall function approach based on a wall law suitable for incompressible turbulent boundary layers under strong adverse pressure gradients is tested. Turn around duct flow characteristics utilizing this modified wall law are presented and compared to results based on a standard wall treatment.
Six months of funding was received for the proposed three year research program (funding for the period from March 1, 1997 to August 31, 1997). Although the official starting date for the project was March 1, 1997, no funding for the project was received until July 1997. In the funded research period, considerable progress was made on Phase I of the proposed research program. The initial research efforts concentrated on applying the 10-, 20-, and 35-moment Gaussian-based closures to a series of standard two-dimensional non-reacting single species test flow problems, such as the flat plate, couette, channel, and rearward facing step flows, and to some other two-dimensional flows having geometries similar to those encountered in chemical-vapor deposition (CVD) reactors. Eigensystem analyses for these systems for the case of two spatial dimensions was carried out and efficient formulations of approximate Riemann solvers have been formulated using these eigenstructures. Formulations to include rotational non-equilibrium effects into the moment closure models for the treatment of polyatomic gases were explored, as the original formulations of the closure models were developed strictly for gases composed of monatomic molecules. The development of a software library and computer code for solving relaxing hyperbolic systems in two spatial dimensions of the type arising from the closure models was also initiated. The software makes use of high-resolution upwind finite-volumes schemes, multi-stage point implicit time stepping, and automatic adaptive mesh refinement (AMR) to solve the governing conservation equations for the moment closures. The initial phase of the code development was completed and a numerical investigation of the solutions of the 10-moment closure model for the simple two-dimensional test cases mentioned above was initiated. Predictions of the 10-moment model were compared to available theoretical solutions and the results of direct-simulation Monte Carlo (DSMC) calculations. The first results of this study were presented at a meeting last year.
An analytical/numerical linear acoustic solution in a nonuniform two-dimensional duct carrying a compressible mean flow is developed. A quasi-one dimensional mean flow model is employed together with a consistent expression for the cross-flow velocity. The acoustic solution is obtained using the Wave Envelope Method. Numerical results are compared with those of an existing Wave Envelope solution which includes a more general mean flow model. In addition, the singular behavior of the solutions derived in the current work for nearly sonic flow conditions is examined explicitly.
A finite difference method for solving the unsteady flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. Solutions are obtained using relaxation procedures. It is determined that there is a limit on reduced frequency, which is a function of Mach number and size of mesh region, above which the relaxation procedures will not converge. It is found that row line relaxation is more efficient than column relaxation and results are presented for a rectangular wing in harmonic pitch.
In this report, we present our findings related to aerodynamic loading of partially inflated balloon shapes. This report will consider aerodynamic loading of partially inflated inextensible natural shape balloons and some relevant problems in potential flow. For the axisymmetric modeling, we modified our Balloon Design Shape Program (BDSP) to handle axisymmetric inextensible ascent shapes with aerodynamic loading. For a few simple examples of two dimensional potential flows, we used the Matlab PDE Toolbox. In addition, we propose a model for aerodynamic loading of strained energy minimizing balloon shapes with lobes. Numerical solutions are presented for partially inflated strained balloon shapes with lobes and no aerodynamic loading.
A one-component laser Doppler velocimeter (LDV) has been used to measure the two-dimensional, periodic flow field about a double circular arc, compressor blade in cascade. Eleven boundary layer profiles were taken on both the pressure and suction surfaces of the blade, and two were taken in the near wake. In this part of the study, the LDV system is described and the suction surface flow field is documented. The suction surface profiles appear to separate both at the leading edge and again somewhat beyond midchord; the leading edge separation apparently reattaches by 2.6 percent chord.
A one-component laser Doppler velocimeter (LDV) has been used to measure the two-dimensional periodic flow field about a double circular arc, compressor blade in cascade. Eleven boundary layer profiles were taken on both the pressure and suction surfaces of the blade, and two profiles were taken in the near wake. In this part of the study, the detailed LDV studies are described. The measurements indicate that the onset of transition occurs near 60 percent chord. The lack of a logarithmic region in the data measured at 97.9 percent chord indicates that transition is not complete. The thin laminar boundary layers near the leading edge led to some measurement problems, characterized by large turbulence intensities, in using the LDV.
Two- and three-dimensional separated flows around cylindrical sections and a body-of-revolution at angles of attack from -10 deg to +20 deg are computed. The blunt-nose-cylinders chosen for the analyses have different configurations, and one of them has a boat-tail. The freestream Mach numbers are 1.5 and 1.6, the unit Reynolds number and the total temperature are 2 million/ft, and 585 R, respectively. Among the possible areas of application for this study are the aerodynamics of separating stores and missiles. The Reynolds-averaged Navier-Stokes equations are solved by an approximately-factored, implicit, upwind-biased, finite-volume algorithm. The convergence to steady state was accelerated using a multigrid strategy. The results helped understanding the structure of the flowfield with varying incidence and configuration, and the suitability of the computational algorithm used for this class of flows. A two-layer algebraic eddy viscosity model is used for the two-dimensional turbulent flows. Laminar three-dimensional calculations are benchmarked through comparisons with wind tunnel test results.
A formula for the determination of equivalent model geometry with two variables measured at the interface is derived, based on two dimensional subsonic flow. This predicted model profile is a reasonable initial estimate for transonic flow as long as the sonic region does not reach the interface. A general formula is given in two forms. One is in terms of complex variable functions and the other is an integral equation. The complex-function formula has the advantage of using analytic expressions. The integral equation form requires a numerical solution after assuming the model geometry as a polynomial function. Examples are given to illustrate the application of the formulas.
The flux-vector and flux-difference splittings of Steger-Warming, van Leer and Roe are tested in all possible combinations on the implicit and explicit operators that can be distinguished in implicit relaxation methods for the steady Euler and Navier-Stokes equations. The tests include one-dimensional inviscid nozzle flow, and two-dimensional inviscid and viscous shock reflection. Roe's splitting, as anticipated, is found to uniformly yield the most accurate results. On the other hand, an approximate Roe splitting of the implicit operator (the complete Roe splitting is too complicated for practical use) proves to be the least robust with regard to convergence to the steady state. In this respect, the Steger-Warming splitting is the most robust; it leads to convergence when combined with any of the splittings in the explicit operator, although not necessarily in the most efficient way.
The flux-vector and flux-difference splittings of Steger-Warming, Van Leer and Roe are tested in all possible combinations in the implicit and explicit operators that can be distinguished in implicit relaxation methods for the steady Euler and Navier-Stokes equations. The tests include one-dimensional inviscid nozzle flow, and two-dimensional inviscid and viscous shock reflection. Roe's splitting, as anticipated, is found to uniformly yield the most accurate results. On the other hand, an approximate Roe splitting of the implicit operator (the complete Roe splitting is too complicated for practical use) proves to be the least robust with regard to convergence to the steady state. In this respect, the Steger-Warming splitting is the most robust: it leads to convergence when combined with any of the splittings in the explicit operator, although not necessarily in the most efficient way.
For many internal transonic flows of practical interest, some of the relevant nondimensional parameters typically are small enough that a perturbation scheme can be expected to give a useful level of numerical accuracy. A variety of steady and unsteady transonic channel and cascade flows is studied with the help of systematic perturbation methods which take advantage of this fact. Asymptotic representations are constructed for small changes in channel cross-section area, small flow deflection angles, small differences between the flow velocity and the sound speed, small amplitudes of imposed oscillations, and small reduced frequencies. Inside a channel the flow is nearly one-dimensional except in thin regions immediately downstream of a shock wave, at the channel entrance and exit, and near the channel throat. A study of two-dimensional cascade flow is extended to include a description of three-dimensional compressor-rotor flow which leads to analytical results except in thin edge regions which require numerical solution. For unsteady flow the qualitative nature of the shock-wave motion in a channel depends strongly on the orders of magnitude of the frequency and amplitude of impressed wall oscillations or fluctuations in back pressure. One example of supersonic flow is considered, for a channel with length large compared to its width, including the effect of separation bubbles and the possibility of self-sustained oscillations. The effect of viscosity on a weak shock wave in a channel is discussed.
The main objective of this research was to develop an efficient three-dimensional computer code for chemically reacting flows. The main computer code developed is ALLSPD-3D. The ALLSPD-3D computer program is developed for the calculation of three-dimensional, chemically reacting flows with sprays. The ALL-SPD code employs a coupled, strongly implicit solution procedure for turbulent spray combustion flows. A stochastic droplet model and an efficient method for treatment of the spray source terms in the gas-phase equations are used to calculate the evaporating liquid sprays. The chemistry treatment in the code is general enough that an arbitrary number of reaction and species can be defined by the users. Also, it is written in generalized curvilinear coordinates with both multi-block and flexible internal blockage capabilities to handle complex geometries. In addition, for general industrial combustion applications, the code provides both dilution and transpiration cooling capabilities. The ALLSPD algorithm, which employs the preconditioning and eigenvalue rescaling techniques, is capable of providing efficient solution for flows with a wide range of Mach numbers. Although written for three-dimensional flows in general, the code can be used for two-dimensional and axisymmetric flow computations as well. The code is written in such a way that it can be run in various computer platforms (supercomputers, workstations and parallel processors) and the GUI (Graphical User Interface) should provide a user-friendly tool in setting up and running the code.
Blade-vortex interaction occurs when a rotor blade encounters the tip vortex from a previous rotor blade. To obtain details of the close encounter process, the results from a flow visualization study of an airfoil representing a rotor blade in the wake of an oscillating airfoil serving as a vortex generator are described. A distinguishing feature of this study is that the vortex filament is oriented parallel to the blade span, orthogonal to the test section free stream velocity. This orientation simulates the case of two-dimensional blade-vortex interaction, which is known to produce the most impulsive and most intensive BVI noise. Photographic data are examined to deduce qualitative and quantitative details of the close encounter interaction process with emphasis on structural changes in the vortex filament and its trajectory.
The primary objective of this research is to extend current capabilities of Large Eddy Simulations (LES) and Direct Numerical Simulations (DNS) for the computational analyses of high speed reacting flows. Our efforts in the first two years of this research have been concentrated on a priori investigations of single-point Probability Density Function (PDF) methods for providing subgrid closures in reacting turbulent flows. In the efforts initiated in the third year, our primary focus has been on performing actual LES by means of PDF methods. The approach is based on assumed PDF methods and we have performed extensive analysis of turbulent reacting flows by means of LES. This includes simulations of both three-dimensional (3D) isotropic compressible flows and two-dimensional reacting planar mixing layers. In addition to these LES analyses, some work is in progress to assess the extent of validity of our assumed PDF methods. This assessment is done by making detailed companions with recent laboratory data in predicting the rate of reactant conversion in parallel reacting shear flows. This report provides a summary of our achievements for the first six months of the third year of this program.
A two-equation k-omega turbulence model has been developed and applied to a quasi-three-dimensional viscous analysis code for blade-to-blade flows in turbomachinery. the code includes the effects of rotation, radius change, and variable stream sheet thickness. The flow equations are given and the explicit runge-Kutta solution scheme is described. the k-omega model equations are also given and the upwind implicit approximate-factorization solution scheme is described. Three cases were calculated: transitional flow over a flat plate, a transonic compressor rotor, and transonic turbine vane with heat transfer. Results were compared to theory, experimental data, and to results using the Baldwin-Lomax turbulence model. The two models compared reasonably well with the data and surprisingly well with each other. Although the k-omega model behaves well numerically and simulates effects of transition, freestream turbulence, and wall roughness, it was not decisively better than the Baldwin-Lomax model for the cases considered here.