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NASA NTRS2001

Filtered Mass Density Function for Design Simulation of High Speed Airbreathing Propulsion Systems

The objective of this research is to develop and implement new methodology for large eddy simulation of (LES) of high-speed reacting turbulent flows. We have just completed two (2) years of Phase I of this research. This annual report provides a brief and up-to-date summary of our activities during the period: September 1, 2000 through August 31, 2001. In the work within the past year, a methodology termed "velocity-scalar filtered density function" (VSFDF) is developed and implemented for large eddy simulation (LES) of turbulent flows. In this methodology the effects of the unresolved subgrid scales (SGS) are taken into account by considering the joint probability density function (PDF) of all of the components of the velocity and scalar vectors. An exact transport equation is derived for the VSFDF in which the effects of the unresolved SGS convection, SGS velocity-scalar source, and SGS scalar-scalar source terms appear in closed form. The remaining unclosed terms in this equation are modeled. A system of stochastic differential equations (SDEs) which yields statistically equivalent results to the modeled VSFDF transport equation is constructed. These SDEs are solved numerically by a Lagrangian Monte Carlo procedure. The consistency of the proposed SDEs and the convergence of the Monte Carlo solution are assessed by comparison with results obtained by an Eulerian LES procedure in which the corresponding transport equations for the first two SGS moments are solved. The unclosed SGS convection, SGS velocity-scalar source, and SGS scalar-scalar source in the Eulerian LES are replaced by corresponding terms from VSFDF equation. The consistency of the results is then analyzed for a case of two dimensional mixing layer.

Drozda, T. G.↗

NASA NTRS2000

An Improved Neutron Transport Algorithm for Space Radiation

A low-energy neutron transport algorithm for use in space radiation protection is developed. The algorithm is based upon a multigroup analysis of the straight-ahead Boltzmann equation by using a mean value theorem for integrals. This analysis is accomplished by solving a realistic but simplified neutron transport test problem. The test problem is analyzed by using numerical and analytical procedures to obtain an accurate solution within specified error bounds. Results from the test problem are then used for determining mean values associated with rescattering terms that are associated with a multigroup solution of the straight-ahead Boltzmann equation. The algorithm is then coupled to the Langley HZETRN code through the evaporation source term. Evaluation of the neutron fluence generated by the solar particle event of February 23, 1956, for a water and an aluminum-water shield-target configuration is then compared with LAHET and MCNPX Monte Carlo code calculations for the same shield-target configuration. The algorithm developed showed a great improvement in results over the unmodified HZETRN solution. In addition, a two-directional solution of the evaporation source showed even further improvement of the fluence near the front of the water target where diffusion from the front surface is important.

Heinbockel, John H.↗

NASA NTRS1999

Emission of Sound From Turbulence Convected by a Parallel Mean Flow in the Presence of a Confining Duct

An approximate method for calculating the noise generated by a turbulent flow within a semi-infinite duct of arbitrary cross section is developed. It is based on a previously derived high-frequency solution to Lilley's equation, which describes the sound propagation in transversely-sheared mean flow. The source term is simplified by assuming the turbulence to be axisymmetric about the mean flow direction. Numerical results are presented for the special case of a ring source in a circular duct with an axisymmetric mean flow. They show that the internally generated noise is suppressed at sufficiently large upstream angles in a hard walled duct, and that acoustic liners can significantly reduce the sound radiated in both the upstream and downstream regions, depending upon the source location and Mach number of the flow.

Goldstein, Marvin E.↗

NASA NTRS1999

Emission of Sound from Turbulence Convected by a Parallel Mean Flow in the Presence of a Confining Duct

An approximate method for calculating the noise generated by a turbulent flow within a semi-infinite duct of arbitrary cross section is developed. It is based on a previously derived high-frequency solution to Lilley's equation, which describes the sound propagation in a transversely-sheared mean flow. The source term is simplified by assuming the turbulence to be axisymmetric about the mean flow direction. Numerical results are presented for the special case of a ring source in a circular duct with an axisymmetric mean flow. They show that the internally generated noise is suppressed at sufficiently large upstream angles in a hard walled duct, and that acoustic liners can significantly reduce the sound radiated in both the upstream and downstream regions, depending upon the source location and Mach number of the flow.

Goldstein, Marvin E.↗

NASA NTRS2018

kL-based Linear and Nonlinear Two-Equation Turbulence Models

The development and implementation of kL-based Reynolds Average Navier-Stokes (RANS) two-equation turbulence models are reported herein. The kL is based on Abdol-Hamid's closure and Menter's modification to Rotta's two-equation model. Rotta shows that a reliable transport equation can be formed from the turbulent length scale L, and the turbulent kinetic energy k. Rotta's kL equation is well suited for term-by-term modeling and displays useful features compared to other scale formulation. One of the important differences is the inclusion of higher order velocity derivatives in the source terms of the scale equation. This can enhance the ability of RANS solvers to simulate unsteady flows in URANS mode. The present report documents the formulation of two model levels of turbulence models as implemented in the computational fluid dynamics FUN3D code. The levels are the two-equation linear k-kL and the two-equation algebraic Reynolds stress model (ARSM). Free shear, separated and corner flow cases are documented and compared with experimental, and other turbulence model data. The results show generally very good comparisons with experimental data. The results from this formulation are similar or better than results using the SST two-equation turbulence model. ARSM shows great promise with similar level of computational resources as basic two-equation turbulence models.

Abdol-Hamid, K. S.↗

NASA NTRS1990

Development of a linearized unsteady aerodynamic analysis for cascade gust response predictions

A method for predicting the unsteady aerodynamic response of a cascade of airfoils to entropic, vortical, and acoustic gust excitations is being developed. Here, the unsteady flow is regarded as a small perturbation of a nonuniform isentropic and irrotational steady background flow. A splitting technique is used to decompose the linearized unsteady velocity into rotational and irrotational parts leading to equations for the complex amplitudes of the linearized unsteady entropy, rotational velocity, and velocity potential that are coupled only sequentially. The entropic and rotational velocity fluctuations are described by transport equations for which closed-form solutions in terms of the mean-flow drift and stream functions can be determined. The potential fluctuation is described by an inhomogeneous convected wave equation in which the source term depends on the rotational velocity field, and is determined using finite-difference procedures. The analytical and numerical techniques used to determine the linearized unsteady flow are outlined. Results are presented to indicate the status of the solution procedure and to demonstrate the impact of blade geometry and mean blade loading on the aerodynamic response of cascades to vortical gust excitations. The analysis described herein leads to very efficient predictions of cascade unsteady aerodynamic response phenomena making it useful for turbomachinery aeroelastic and aeroacoustic design applications.

Verdon, Joseph M.↗

NASA NTRS2018

Development and Documentation of kL-Based Linear, Nonlinear, and Full Reynolds Stress Turbulence Models

The development and implementation of kL-based Reynolds Average Navier-Stokes (RANS) turbulence models are reported herein. The kL is based on Abdol-Hamid's closure and Menter's modi cation to Rotta's two-equation model. Rotta shows that a reliable transport equation can be formed from the turbulent length scale L, and the turbulent kinetic energy k. Rotta's kL equation is well suited for term-by-term modeling and displays useful features compared to other scale formulation. One of the important di erences is the inclusion of higher order velocity derivatives in the source terms of the scale equation. This can enhance the ability of RANS solvers to simulate unsteady ows in URANS mode. The present report documents the formulation of three model levels of turbulence models as implemented in the CFD code FUN3D. Methodology and calibration examples are shown in detail. The levels are the linear k-kL and the two-equation algebraic Reynolds stress model (ARSM) as well as the full Reynolds Stress Model (RSM). Attached, separated and corner ow cases are documented and compared with experimental, theoretical and other turbulence model data. The results show generally very good comparisons with canonical and experimental data. The results from this formulation are similar or better than results using the SST two- equation turbulence model. ARSM shows great promise with similar level of computational resources as general two equation turbulence models.

Abdol-Hamid, Khaled S.↗

NASA NTRS2017

Implementation of a Body Force Model in OVERFLOW for Propulsor Simulations

We present an implementation of a propulsor model based on body force method into the OVERFLOW computational fluid dynamics code to model turbofan engines and propulsors of similar type. The model estimates the forces imparted on the fluid by the blade camber surfaces as a body force source terms in the momentum and energy equations over grids that represent the rotor and stator of a fan stage. We tested the implementation on three cases: 1) Source Diagnostics Test (SDT) fan with R4 rotors, which has extensive test data on aerodynamic performance and rotor wake surveys, 2) A stand-alone Aeronaut TF8000 propulsor which is an off-the-shelf propulsor used on model aircraft and 3) The D8 aircraft model with TF8000 propulsors placed in a wind tunnel. Despite missing some of the features in the velocity profiles near the endwalls (i.e. hub and casing surfaces), the OVERFLOW simulations with body force model predicted area-averaged flow speed and total pressure rise through the SDT propulsor within a few percent of the LDV (Laser Doppler Velocimetry) measurements. In the case of TF8000 propulsor on the D8 airframe, the model under-predicted mechanical power coefficient by several percent of the wind tunnel test results when the horizontal force balance condition over the airframe is targeted by tuning rotor speed. By investigating the upstream influence of the rotor swirl, it was found out that the induced swirl velocity effects upstream were relatively small and they rapidly vanished before reaching one fan diameter upstream of the fan face. The body force model provided insights on aerothermodynamics and aeromechanics of boundary layer ingesting propulsor; these insights could not be obtained by using the uniform pressure jump model.

Propulsor↗

NASA NTRS2020

Multigrid Preconditioning for a Space-Time Spectral-Element Discontinuous-Galerkin Solver

In this work we examine a multigrid preconditioning approach in the context of a high- order tensor-product discontinuous-Galerkin spectral-element solver. We couple multigrid ideas together with memory lean and efficient tensor-product preconditioned matrix-free smoothers. Block ILU(0)-preconditioned GMRES smoothers are employed on the coarsest spaces. The performance is evaluated on nonlinear problems arising from unsteady scale- resolving solutions of the Navier-Stokes equations: separated low-Mach unsteady ow over an airfoil from laminar to turbulent ow. A reduction in the number of ne space iterations is observed, which proves the efficiency of the approach in terms of preconditioning the linear systems, however this gain was not reflected in the CPU time. Finally, the preconditioner is successfully applied to problems characterized by stiff source terms such as the set of RANS equations, where the simple tensor product preconditioner fails. Theoretical justification about the findings is reported and future work is outlined.

Franciolini, Matteo↗

NASA NTRS2020

Juncture Flow Computations using kL-Based Turbulence Models

The development and implementation of kL-based Reynolds-Average Navier-Stokes (RANS) two-equation turbulence models are reported in this paper. The kL model is based on Abdol-Hamid's closure and Menter's modification to Rotta's two-equation model. Rotta showed that a reliable transport equation can be formed from the turbulence length scale L, and the turbulence kinetic energy k. Rotta's kL equation is well suited for a term-by-term modeling and displays useful features compared to other scale formulations. One of the important differences is the inclusion of higher-order velocity derivatives in the source terms of the scale equation. This can enhance the ability of RANS solvers to simulate unsteady flows in URANS mode. The k-kL scheme has been modified to include the Algebraic Reynolds Stress Model (ARSM) and the Quadratic Constitutive Relation (QCR) as nonlinear models. These models have gone through extensive validations using two-dimensional benchmark problems. The present study documents the application of the k-kL schemes to simulate flow around the Juncture Flow Model (JFM). The k-kL prediction results show generally good comparisons with measurements. The results from this formulation are similar to, or better than results using the SA-RC-QCR2000 two-equation turbulence model. The ARSM and the QCR formulations of k-kL show promise with a similar level of computational resources as basic two-equation turbulence models.

K S Abdol-Hamid↗

NASA NTRS1990

Gust response analysis for cascades operating in nonuniform mean flows

The linearized unsteady aerodynamic response of a cascade of airfoils subjected to entropic, vortical, and acoustic gusts is analyzed. Field equations for the first-order unsteady perturbation flow are obtained by linearizing the full time-dependent mass, momentum, and energy conservation equations about a nonlinear, isentropic, and irrotational mean or steady flow. A splitting technique is then used to decompose the unsteady velocity field into irrotational and rotational parts leading to field equations for the unsteady entropy, rotational velocity, and irrotational velocity fluctuations that are coupled only sequentially. The entropic and rotational velocity fluctuations can be described in terms of the mean-flow drift and stream functions which can be computed numerically. The irrotational unsteady velocity is described by an inhomogeneous linearized potential equation which contains a source term that depends on the rotational velocity field. This equation is solved via a finite difference technique. Results are presented to indicate the status of the numerical solution procedure and to demonstrate the impact of blade geometry and mean blade loading on the aerodynamic response of cascades to vortical gust excitations. The analysis described leads to very efficient predictions of cascade unsteady aerodynamic phenomena making it useful for turbomachinery aeroelastic and aeroacoustic design applications.

Hall, Kenneth C.↗

NASA NTRS1991

Gust response analysis for cascades operating in nonuniform mean flows

The linearized unsteady aerodynamic response of a cascade of airfoils subjected to entropic, vortical, and acoustic gusts is analyzed. Field equations for the first-order unsteady perturbation flow are obtained by linearizing the full time-dependent mass, momentum, and energy conservation equations about a nonlinear, isentropic, and irrotational mean or steady flow. A splitting technique is then used to decompose the unsteady velocity field into irrotational and rotational parts leading to field equations for the unsteady entropy, rotational velocity, and irrotational velocity fluctuations that are coupled only sequentially. The entropic and rotational velocity fluctuations can be described in terms of the mean-flow drift and stream functions which can be computed numerically. The irrotational unsteady velocity is described by an inhomogeneous linearized potential equation which contains a source term that depends on the rotational velocity field. This equation is solved via a finite difference technique. Results are presented to indicate the status of the numerical solution procedure and to demonstrate the impact of blade geometry and mean blade loading on the aerodynamic response of cascades to vortical gust excitations. The analysis described leads to very efficient predictions of cascade unsteady aerodynamics phenomena making it useful for turbomachinery aeroelastic and aeroacoustic design applications.

Hall, Kenneth C.↗

NASA NTRS1994

Space simulation techniques and facilities for SAX STM test campaign

SAX is a satellite for X-Ray astronomy. It is a major element of the overall basic Science Program of the Italian Space Agency (ASI) and is being developed with the contribution of the Netherlands Agency for Aerospace Programs (NIVR). The scientific objectives of SAX are to carry out systematic and comprehensive observations of celestial X-Ray sources over the 0.1 - 300 KeV energy range with special emphasis on spectral and timing measurements. The satellite will also monitor the X-Ray sky to investigate long-term source variability and to permit localization and study of X-Ray transients. Alenia Spazio is developing the satellite that is intended for launch in the second half of 1995 in a low, near-equatorial Earth orbit. At system level a Structural Thermal Model (STM) has been conceived to verify the environmental requirements by validating the mechanical and thermal analytical models and qualifying satellite structure and thermal control. In particular, the following tests have been carried out in Alenia Spazio, CEA/CESTA and ESTEC facilities: Modal Survey, Centrifuge, Acoustic, Sinusoidal/Random Vibration and Thermal Balance. The paper, after a short introduction of the SAX satellite, summarizes the environmental qualification program performed on the SAX STM. It presents test objectives, methodologies and relevant test configurations. Peculiar aspects of the test campaign are highlighted. Problems encountered and solutions adopted in performing the tests are described as well. Furthermore, test results are presented and assessed.

Giordano, Pietro↗

NASA NTRS2013

Assessments of a Turbulence Model Based on Menter's Modification to Rotta's Two-Equation Model

The main objective of this paper is to construct a turbulence model with a more reliable second equation simulating length scale. In the present paper, we assess the length scale equation based on Menter s modification to Rotta s two-equation model. Rotta shows that a reliable second equation can be formed in an exact transport equation from the turbulent length scale L and kinetic energy. Rotta s equation is well suited for a term-by-term modeling and shows some interesting features compared to other approaches. The most important difference is that the formulation leads to a natural inclusion of higher order velocity derivatives into the source terms of the scale equation, which has the potential to enhance the capability of Reynolds-averaged Navier-Stokes (RANS) to simulate unsteady flows. The model is implemented in the PAB3D solver with complete formulation, usage methodology, and validation examples to demonstrate its capabilities. The detailed studies include grid convergence. Near-wall and shear flows cases are documented and compared with experimental and Large Eddy Simulation (LES) data. The results from this formulation are as good or better than the well-known SST turbulence model and much better than k-epsilon results. Overall, the study provides useful insights into the model capability in predicting attached and separated flows.

Abdol-Hamid, Khaled S.↗

NASA NTRS1991

Computation of supersonic jet mixing noise for an axisymmetric CD nozzle using k-epsilon turbulence model

The turbulent mixing noise of a supersonic jet is calculated for a round convergent-divergent nozzle at the design pressure ratio. Aerodynamic computations are performed using the PARC code with a k-epsilon turbulence model. Lighthill's acoustic analogy combined with Ribner's assumption is adopted. The acoustics solution is based upon the methodology followed by GE in the MGB code. The source correlation function is expressed as a linear combination of second-order tensors. Assuming separable second-order correlations and incorporating Batchelor's isotropic turbulence model, the source term was calculated from the kinetic energy of turbulence. A Gaussian distribution for the time-delay of correlation was introduced. The computational fluid dynamics (CFD) solution was used to obtain the source strength as well as the characteristic time-delay of correlation. The effect of sound/flow interaction was incorporated using the high frequency asymptotic solution to Lilley's equation for axisymmetric geometries. Acoustic results include sound pressure level directivity and spectra at different polar angles. The aerodynamic and acoustic results demonstrate favorable agreement with experimental data.

Khavaran, Abbas↗

NASA NTRS1992

Computation of supersonic jet mixing noise for an axisymmetric CD nozzle using k-epsilon turbulence model

Khavaran, A.↗

NASA NTRS1996

A Computer Program for the Computation of Running Gear Temperatures Using Green's Function

A new technique has been developed to study two dimensional heat transfer problems in gears. This technique consists of transforming the heat equation into a line integral equation with the use of Green's theorem. The equation is then expressed in terms of eigenfunctions that satisfy the Helmholtz equation, and their corresponding eigenvalues for an arbitrarily shaped region of interest. The eigenfunction are obtalned by solving an intergral equation. Once the eigenfunctions are found, the temperature is expanded in terms of the eigenfunctions with unknown time dependent coefficients that can be solved by using Runge Kutta methods. The time integration is extremely efficient. Therefore, any changes in the time dependent coefficients or source terms in the boundary conditions do not impose a great computational burden on the user. The method is demonstrated by applying it to a sample gear tooth. Temperature histories at representative surface locatons are given.

GREENS FUNCTIONS↗

NASA NTRS1996

Multigrid Method for Modeling Multi-Dimensional Combustion with Detailed Chemistry

A highly accurate and efficient numerical method is developed for modeling 3-D reacting flows with detailed chemistry. A contravariant velocity-based governing system is developed for general curvilinear coordinates to maintain simplicity of the continuity equation and compactness of the discretization stencil. A fully-implicit backward Euler technique and a third-order monotone upwind-biased scheme on a staggered grid are used for the respective temporal and spatial terms. An efficient semi-coarsening multigrid method based on line-distributive relaxation is used as the flow solver. The species equations are solved in a fully coupled way and the chemical reaction source terms are treated implicitly. Example results are shown for a 3-D gas turbine combustor with strong swirling inflows.

Zheng, Xiaoqing↗