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NASA NTRS1985

Simulation of Multistage Turbine Flows

The numerical simulation of turbine flows serves to enhance the understanding of the flow phenomena within multistage turbomachinery components. The direct benefit of this activity is improved modeling capability, which can be used to improve component efficiency and durability. A hierarchy of equations was formulated to assess the difficulty in analyzing the flow field within multistage turbomachinery components. The Navier-Stokes equations provides the most complete description. The simplest description is given by a set of equations that govern the quasi-one-dimensional flow. The number of unknowns to be solved for increases monotonically above the number of equations. The development of the additional set of equations needed to mathematically close the system of equations forms the closure problem associated with that level of description. For the Navier-Stokes equation there is no closure problem. For the quasi-one-dimensional equation set random flow fluctuations, unsteady fluctuations, nonaxisymmetric flow variations, and hub-to-shroud variations on the quasi-one-dimensional flow must be accounted for.

Celestina, M. L.↗

NASA NTRS1997

Large Scale Turbulent Structures in Supersonic Jets

Jet noise is a major concern in the design of commercial aircraft. Studies by various researchers suggest that aerodynamic noise is a major contributor to jet noise. Some of these studies indicate that most of the aerodynamic jet noise due to turbulent mixing occurs when there is a rapid variation in turbulent structure, i.e. rapidly growing or decaying vortices. The objective of this research was to simulate a compressible round jet to study the non-linear evolution of vortices and the resulting acoustic radiations. In particular, to understand the effect of turbulence structure on the noise. An ideal technique to study this problem is Direct Numerical Simulations(DNS), because it provides precise control on the initial and boundary conditions that lead to the turbulent structures studied. It also provides complete 3-dimensional time dependent data. Since the dynamics of a temporally evolving jet are not greatly different from those, of a spatially evolving jet, a temporal jet problem was solved, using periodicity ill the direction of the jet axis. This enables the application of Fourier spectral methods in the streamwise direction. Physically this means that turbulent structures in the jet are repeated in successive downstream cells instead of being gradually modified downstream into a jet plume. The DNS jet simulation helps us understand the various turbulent scales and mechanisms of turbulence generation in the evolution of a compressible round jet. These accurate flow solutions will be used in future research to estimate near-field acoustic radiation by computing the total outward flux across a surface and determine how it is related to the evolution of the turbulent solutions. Furthermore, these simulations allow us to investigate the sensitivity of acoustic radiations to inlet/boundary conditions, with possible application to active noise suppression. In addition, the data generated can be used to compute various turbulence quantities such as mean velocities, turbulent stresses, etc. which will aid in turbulence modeling. This report will be presented in two chapters. The first chapter describes some work on the linear stability of a supersonic round jet and the implications of this for the jet noise problem. The second chapter is an extensive discussion of numerical work using the spectral method which we use to solve the compressible Navier-Stokes equations to study turbulent jet flows. The method uses Fourier expansions in the azimuthal and streamwise direction and a 1-D B-spline basis representation in the radial direction. The B-spline basis is locally supported and this ensures block diagonal matrix equations which can be solved in O(N) steps. This is a modification of a boundary layer code developed by Robert Moser. A very accurate highly resolved Direct Numerical Simulation (DNS) of a turbulent jet flow is produced.

Rao, Ram Mohan↗

NASA NTRS1997

Large Scale Turbulent Structures in Supersonic Jets

Jet noise is a major concern in the design of commercial aircraft. Studies by various researchers suggest that aerodynamic noise is a major contributor to jet noise. Some of these studies indicate that most of the aerodynamic jet noise due to turbulent mixing occurs when there is a rapid variation in turbulent structure, i.e. rapidly growing or decaying vortices. The objective of this research was to simulate a compressible round jet to study the non-linear evolution of vortices and the resulting acoustic radiations. In particular, to understand the effect of turbulence structure on the noise. An ideal technique to study this problem is Direct Numerical Simulations (DNS), because it provides precise control on the initial and boundary conditions that lead to the turbulent structures studied. It also provides complete 3-dimensional time dependent data. Since the dynamics of a temporally evolving jet are not greatly different from those of a spatially evolving jet, a temporal jet problem was solved, using periodicity in the direction of the jet axis. This enables the application of Fourier spectral methods in the streamwise direction. Physically this means that turbulent structures in the jet are repeated in successive downstream cells instead of being gradually modified downstream into a jet plume. The DNS jet simulation helps us understand the various turbulent scales and mechanisms of turbulence generation in the evolution of a compressible round jet. These accurate flow solutions will be used in future research to estimate near-field acoustic radiation by computing the total outward flux across a surface and determine how it is related to the evolution of the turbulent solutions. Furthermore, these simulations allow us to investigate the sensitivity of acoustic radiations to inlet/boundary conditions, with possible appli(,a- tion to active noise suppression. In addition, the data generated can be used to compute, various turbulence quantities such as mean velocities, turbulent stresses, etc. which will aid in turbulence modeling. This report will be presented in two chapters. The first chapter describes some work on the linear stability of a supersonic round jet and the implications of this for the jet noise problem. The second chapter is an extensive discussion of numerical work using the spectral method which we use to solve the compressible Navier-Stokes equations to study turbulent jet flows. The method uses Fourier expansions in the azimuthal and streamwise direction and a 1-D B-spline basis representation in the radial direction. The B-spline basis is locally supported and this ensures block diagonal matrix equations which can be solved in O(N) steps. This is a modification of a boundary layer code developed by Robert Moser. A very accurate highly resolved DNS of a turbulent jet flow is produced.

Rao, Ram Mohan↗

NASA NTRS1988

A diagonally inverted LU implicit multigrid scheme for the 3-D Navier-Stokes equations and a two equation model of turbulence

An LU implicit multigrid algorithm is developed to calculate 3-D compressible viscous flows. This scheme solves the full 3-D Reynolds-Averaged Navier-Stokes equation with a two-equation kappa-epsilon model of turbulence. The flow equations are integrated by an efficient, diagonally inverted, LU implicit multigrid scheme while the kappa-epsilon equations are solved, uncoupled from the flow equations, by a block LU implicit algorithm. The flow equations are solved within the framework of the multigrid method using a four-grid level W-cycle, while the kappa-epsilon equations are iterated only on the finest grid. This treatment of the Reynolds-Averaged Navier-Stokes equations proves to be an efficient method for calculating 3-D compressible viscous flows.

Yokota, Jeffrey W.↗

NASA NTRS1989

A diagonally inverted LU implicit multigrid scheme for the 3-D Navier-Stokes equations and a two equation model of turbulence

Yokota, Jeffrey W.↗

NASA NTRS1992

Solution of the Burnett equations for hypersonic flows near the continuum limit

The INCA code, a three-dimensional Navier-Stokes code for analysis of hypersonic flowfields, was modified to analyze the lower reaches of the continuum transition regime, where the Navier-Stokes equations become inaccurate and Monte Carlo methods become too computationally expensive. The two-dimensional Burnett equations and the three-dimensional rotational energy transport equation were added to the code and one- and two-dimensional calculations were performed. For the structure of normal shock waves, the Burnett equations give consistently better results than Navier-Stokes equations and compare reasonably well with Monte Carlo methods. For two-dimensional flow of Nitrogen past a circular cylinder the Burnett equations predict the total drag reasonably well. Care must be taken, however, not to exceed the range of validity of the Burnett equations.

Imlay, Scott T.↗

NASA NTRS1992

A study of juncture flow in the NASA Langley 0.3-meter transonic cryogenic tunnel

A numerical investigation of the interaction between a wind tunnel sidewall boundary layer and a thin low-aspect-ratio wing has been performed for transonic speeds and flight Reynolds numbers. A three-dimensional Navier-Stokes code was applied to calculate the flow field. The first portion of the investigation examined the capability of the code to calculate the flow around the wing, with no sidewall boundary layer present. The second part of the research examined the effect of modeling the sidewall boundary layer. The results indicated that the sidewall boundary layer had a strong influence on the flow field around the wing. The viscous sidewall computations accurately predicted the leading edge suction peaks, and the strong adverse pressure gradients immediately downstream of the leading edge. This was in contrast to the consistent underpredictions of the free-air computations. The low momentum of the sidewall boundary layer resulted in higher pressures in the juncture region, which decreased the favorable spanwise pressure gradient. This significantly decreased the spanwise migration of the wing boundary layer. The computations indicated that the sidewall boundary layer remained attached for all cases examined. Weak vortices were predicted in both the upper and lower surface juncture regions. These vortices are believed to have been generated by lateral skewing of the streamlines in the approaching boundary layer.

Chokani, Ndaona↗

NASA NTRS1980

Three-layer interactive method for computing supersonic laminar separated flows

An interactive model for numerical computation of complicated two-dimensional flowfields including regions of reversed flow is proposed. The present approach is one of dividing the flowfield into three regions, in each of which a simplified mathematical model is applied: (1) outer, supersonic flow for which the full potential equation (hyperbolic) is used; (2) viscous, laminar layer in which the compressible boundary-layer model (parabolic) is used; and (3) recirculating flow modeled by the incompressible Navier-Stokes equations (elliptic). For matching of the numerical solutions in the three layers, two interaction models are developed: one for pressure interaction, the other for interaction between the shear layer and the recirculating flow. The uniform solution for the whole flowfield is then obtained by iteration of the local solutions under the constraints imposed by matching. The three-layer interactive model is used for solution of the flowfield past an asymmetric cavity. The method is shown to be capable of dealing with backflow without encountering problems at separation, characteristic to the boundary-layer approach.

Brandeis, J.↗

NASA NTRS1989

Application of multi-grid methods for solving the Navier-Stokes equations

This paper presents the application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems. The methods consists of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line- or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to those of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.

Demuren, A. O.↗

NASA NTRS1952

Generalization of Boundary-Layer Momentum-Integral Equations to Three-Dimensional Flows Including Those of Rotating System

The Navier-Stokes equations of motion and the equation of continuity are transformed so as to apply to an orthogonal curvilinear coordinate system rotating with a uniform angular velocity about an arbitrary axis in space. A usual simplification of these equations as consistent with the accepted boundary-layer theory and an integration of these equations through the boundary layer result in boundary-layer momentum-integral equations for three-dimensional flows that are applicable to either rotating or nonrotating fluid boundaries. These equations are simplified and an approximate solution in closed integral form is obtained for a generalized boundary-layer momentum-loss thickness and flow deflection at the wall in the turbulent case. A numerical evaluation of this solution carried out for data obtained in a curving nonrotating duct shows a fair quantitative agreement with the measures values. The form in which the equations are presented is readily adaptable to cases of steady, three-dimensional, incompressible boundary-layer flow like that over curved ducts or yawed wings; and it also may be used to describe the boundary-layer flow over various rotating surfaces, thus applying to turbomachinery, propellers, and helicopter blades.

Mager, Arthur↗

NASA NTRS1977

Finite element analysis of aeroacoustic jet-flap flows

A computational analysis was performed on the steady, turbulent aerodynamic flowfields associated with a jet-blown flap. For regions devoid of flow separation, a parabolic approximation to the governing time-averaged Navier-Stokes equations was applied. Numerical results are presented for the symmetry plane flow of a slot-nozzle planar jet flap geometry, including prediction of flowfield evolution within the secondary mixing region immediately downstream of the trailing edge. Using a two equation turbulence kinetic energy closure model, rapid generation and decay of large spatial gradients in mean and correlated fluctuating velocity components within the immediate wake region were predicted. Modifications to the turbulent flow structure, as induced by porous surface treatment of the flap, were evaluated. The recirculating flow within a representative discrete slot in the surface was evaluated, using the two dimensional, time-averaged Navier-Stokes equations.

Baker, A. J.↗

NASA NTRS1990

Numerical computation of viscous flow about unconventional airfoil shapes

A new two-dimensional computer code was developed to analyze the viscous flow around unconventional airfoils at various Mach numbers and angles of attack. The Navier-Stokes equations are solved using an implicit, upwind, finite-volume scheme. Both laminar and turbulent flows can be computed. A new nonequilibrium turbulence closure model was developed for computing turbulent flows. This two-layer eddy viscosity model was motivated by the success of the Johnson-King model in separated flow regions. The influence of history effects are described by an ordinary differential equation developed from the turbulent kinetic energy equation. The performance of the present code was evaluated by solving the flow around three airfoils using the Reynolds time-averaged Navier-Stokes equations. Excellent results were obtained for both attached and separated flows about the NACA 0012 airfoil, the RAE 2822 airfoil, and the Integrated Technology A 153W airfoil. Based on the comparison of the numerical solutions with the available experimental data, it is concluded that the present code in conjunction with the new nonequilibrium turbulence model gives excellent results.

Ahmed, S.↗

NASA NTRS1986

The effect of fluid flow due to the crystal-melt density change on the growth of a parabolic isothermal dendrite

The Ivantsov (1947) analysis of an isolated isothermal dendrite (with zero surface tension) growing into a supercooled liquid is extended to include the effects of the fluid flow due to volume contraction or expansion upon solidification. For an axisymmetric paraboloidal dendrite, an analytic solution to the Navier-Stokes equations is obtained. The magnitude of the flow is proportional to the relative density change epsilon, and the flow becomes negligible far from the surface of the dendrite. The temperature field consistent with this flow can also be found explicitly. The well-known expression that relates the dimensionless supercooling to the Peclet number in the absence of fluid flow is modified for nonzero epsilon, but the effect is of order epsilon and hence is seen to be minor for most values of epsilon and dimensionless supercooling that occur in practice.

Mcfadden, G. B.↗

NASA NTRS1987

Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier-Stokes equations

The current status of streamline-upwind/Petrov-Galerkin (SUPG) methods for the analysis of flow problems is surveyed in an analytical review. Problem areas addressed include classical Galerkin, upwind, artificial-diffusion, SUPG, discontinuous Galerkin, space-time FEM, and discontinuity-capturing approaches to the scalar advection-diffusion equation; incompressible flows; advective-diffusive systems; and the compressible Euler and Navier-Stokes equations. Graphs and diagrams are provided, and the good stability properties of state-of-the-art SUPG methods are pointed out.

Hughes, Thomas J. R.↗

NASA NTRS1989

Computations of three-dimensional steady and unsteady viscous incompressible flows

The INS3D family of computational fluid dynamics computer codes is presented. These codes are used to as tools in developing and assessing algorithms for solving the incompressible Navier-Stokes equations for steady-state and unsteady flow problems. This work involves applying the codes to real-world problems involving complex three-dimensional geometries. The algorithms utilized include the method of pseudocompressibility including both central and upwind differencing, several types of artificial dissipation schemes, approximate factorization, and an implicit line-relaxation scheme. These codes have been validated using a wide range of problems including flow over a backward-facing step, driven cavity flow, flow through various types of ducts, and steady and unsteady flow over a circular cylinder. Many diverse flow applications have been solved using these codes including parts of the Space Shuttle Main Engine, problems in naval hydrodynamics, low-speed aerodynamics, and biomedical fluid flows. The presentation details several of these, including the flow through a Space Shuttle Main Engine inducer, vortex shedding behind a circular cylinder, and flow through an artificial heart.

Kwak, Dochan↗

NASA NTRS1979

Computation of three-dimensional turbulent separated flows at supersonic speeds

Numerical solutions of the time-averaged Navier-Stokes equations employing a simple eddy-viscosity model have been obtained for three dimensional turbulent flow fields at supersonic speeds. The computer results are compared with a series of experimental test flows describing the interaction of a swept shock wave with a turbulent boundary layer for various shock-wave strengths. Very good agreement is obtained between the computed and experimental surface and flow-field results. The computed flow fields are examined in detail to investigate the physics of this type of flow field. Questions concerning the existence of a vortex and the relationship between converging surface oil streaks and the resulting flow field are addressed.

Horstman, C. C.↗

NASA NTRS1988

Numerical simulation methods of incompressible flows and an application to the space shuttle main engine

Incompressible Navier-Stokes solution methods are discussed with an emphasis on the pseudocompressibility method. A steady-state flow solver based on the pseudocompressibility approach is then described. This flow-solver code was used to analyze the internal flow in the Space Shuttle main engine hot-gas manifold. Salient features associated with this three-dimensional realistic flow simulation are discussed. Numerical solutions relevant to the current engine analysis and the redesign effort are discussed along with experimental results. This example demonstrates the potential of computational fluid dynamics as a design tool for aerospace applications.

Chang, J. L. C.↗

NASA NTRS1987

Calculating rotordynamic coefficients of seals by finite-difference techniques

For modelling the turbulent flow in a seal the Navier-Stokes equations in connection with a turbulence (kappa-epsilon) model are solved by a finite-difference method. A motion of the shaft round the centered position is assumed. After calculating the corresponding flow field and the pressure distribution, the rotor-dynamic coefficients of the seal can be determined. These coefficients are compared with results obtained by using the bulk flow theory of Childs and with experimental results.

Dietzen, F. J.↗