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NASA NTRS1975

A theoretical evaluation of rigid baffles in suppression of combustion instability

An analytical technique for the prediction of the effects of rigid baffles on the stability of liquid propellant combustors is presented. This analysis employs both two and three dimensional combustor models characterized by concentrated combustion sources at the chamber injector and a constant Mach number nozzle. An eigenfunction-matching method is used to solve the linearized partial differential equations describing the unsteady flow field for both models. Boundary layer corrections to this unsteady flow are used in a mechanical energy dissipation model to evaluate viscous and turbulence effects within the flow. An integral stability relationship is then employed to predict the decay rate of the oscillations. Results of this analysis agree qualitatively with experimental observations and show that sufficient dissipation exists to indicate that the proper mechanism of baffle damping is a fluid dynamic loss.

Combustion instability↗

NASA NTRS1996

Reduced Stress Tensor and Dissipation and the Transport of Lamb Vector

We develop a methodology to ensure that the stress tensor, regardless of its number of independent components, can be reduced to an exactly equivalent one which has the same number of independent components as the surface force. It is applicable to the momentum balance if the shear viscosity is constant. A direct application of this method to the energy balance also leads to a reduction of the dissipation rate of kinetic energy. Following this procedure, significant saving in analysis and computation may be achieved. For turbulent flows, this strategy immediately implies that a given Reynolds stress model can always be replaced by a reduced one before putting it into computation. Furthermore, we show how the modeling of Reynolds stress tensor can be reduced to that of the mean turbulent Lamb vector alone, which is much simpler. As a first step of this alternative modeling development, we derive the governing equations for the Lamb vector and its square. These equations form a basis of new second-order closure schemes and, we believe, should be favorably compared to that of traditional Reynolds stress transport equation.

Wu, Jie-Zhi↗

NASA NTRS1998

Improved Modeling of Finite-Rate Turbulent Combustion Processes in Research Combustors

The objective of this thesis is to further develop and test a stochastic model of turbulent combustion in recirculating flows. There is a requirement to increase the accuracy of multi-dimensional combustion predictions. As turbulence affects reaction rates, this interaction must be more accurately evaluated. In this work a more physically correct way of handling the interaction of turbulence on combustion is further developed and tested. As turbulence involves randomness, stochastic modeling is used. Averaged values such as temperature and species concentration are found by integrating the probability density function (pdf) over the range of the scalar. The model in this work does not assume the pdf type, but solves for the evolution of the pdf using the Monte Carlo solution technique. The model is further developed by including a more robust reaction solver, by using accurate thermodynamics and by more accurate transport elements. The stochastic method is used with Semi-Implicit Method for Pressure-Linked Equations. The SIMPLE method is used to solve for velocity, pressure, turbulent kinetic energy and dissipation. The pdf solver solves for temperature and species concentration. Thus, the method is partially familiar to combustor engineers. The method is compared to benchmark experimental data and baseline calculations. The baseline method was tested on isothermal flows, evaporating sprays and combusting sprays. Pdf and baseline predictions were performed for three diffusion flames and one premixed flame. The pdf method predicted lower combustion rates than the baseline method in agreement with the data, except for the premixed flame. The baseline and stochastic predictions bounded the experimental data for the premixed flame. The use of a continuous mixing model or relax to mean mixing model had little effect on the prediction of average temperature. Two grids were used in a hydrogen diffusion flame simulation. Grid density did not effect the predictions except for peak temperature and tangential velocity. The hybrid pdf method did take longer and required more memory, but has a theoretical basis to extend to many reaction steps which cannot be said of current turbulent combustion models.

VanOverbeke, Thomas J.↗

NASA NTRS1981

Prediction of swirling reacting flow in ramjet combustors

Numerical computations have been undertaken for a basic two-dimensional axisymmetric flowfield which is similar to that found in conventional gas turbine and ramjet combustors. A swirling flow enters a larger chamber via a sudden or gradual expansion. The calculation method involves a staggered grid system for axial and radial velocities, a line relaxation procedure for efficient solution of the equations, a two-equation turbulence energy-turbulence dissipation rate turbulence model, a stairstep boundary representation of the expansion flow, and realistic accommodation of swirl effects. The results include recirculation zone characterization and predicted mean streamline patterns. Predictions with and without chemical reaction are obtained. An associated isothermal experimental flow study is providing a useful data base. Successful outcomes of the work can be incorporated into the more combustion- and hardware-oriented activities of industrial concerns.

Lilley, D. G.↗

NASA NTRS1994

Developments and applications of dynamic models for large eddy simulation of complex flows

The dynamic modeling procedure for large eddy simulation of turbulent flows is reviewed and recent developments in the theoretical aspects and applications are described. Methods for inclusion of backscatter of energy from small to large scale motions are presented. New formulations of the dynamic procedure are proposed which are optimized based on the subgrid scale flux vector or the energy dissipation rate instead of the subgrid scale stress tensor. Recent results from application of the model to forced isotropic turbulence with an inertial subrange, flow over a backward facing step at Reynolds number of 28000, and flow over a concave curved surface are presented.

Moin, P.↗

NASA NTRS1993

Computation of the sound generated by isotropic turbulence

The acoustic radiation from isotropic turbulence is computed numerically. A hybrid direct numerical simulation approach which combines direct numerical simulation (DNS) of the turbulent flow with the Lighthill acoustic analogy is utilized. It is demonstrated that the hybrid DNS method is a feasible approach to the computation of sound generated by turbulent flows. The acoustic efficiency in the simulation of isotropic turbulence appears to be substantially less than that in subsonic jet experiments. The dominant frequency of the computed acoustic pressure is found to be somewhat larger than the dominant frequency of the energy-containing scales of motion. The acoustic power in the simulations is proportional to epsilon (M(sub t))(exp 5) where epsilon is the turbulent dissipation rate and M(sub t) is the turbulent Mach number. This is in agreement with the analytical result of Proudman (1952), but the constant of proportionality is smaller than the analytical result. Two different methods of computing the acoustic power from the DNS data bases yielded consistent results.

Sarkar, S.↗

NASA NTRS1993

SWIRL as a means of liquid management in low gravity

Swirling of a liquid in a container may prove to be a more desirable method of managing liquids in low gravity (space) environments than by rotating the entire container. By injecting a relatively high velocity liquid tangentially into the body of the fluid, swirl can best be started rapidly, however an estimate of the quantity and velocity of jetflow, or mechanical power of a pump impeller required to maintain a given radial acceleration (G force) is needed to assess the feasibility of such a method. While the key aspect of the problem is determining the rate of rotational energy dissipation by wall friction in the container, there are other considerations, and the present study investigates the possible additional effects of axial variation of tangential velocity and secondary (radial and axial) flow components within the rotating fluid.

Steward, W. Gene↗

NASA NTRS1986

Computation of turbulent boundary layer flows with an algebraic stress turbulence model

An algebraic stress turbulence model is presented, characterized by the following: (1) the eddy viscosity expression is derived from the Reynolds stress turbulence model; (2) the turbulent kinetic energy dissipation rate equation is improved by including a production range time scale; and (3) the diffusion coefficients for turbulence equations are adjusted so that the kinetic energy profile extends further into the free stream region found in most experimental data. The turbulent flow equations were solved using a finite element method. Examples include: fully developed channel flow, fully developed pipe flow, flat plate boundary layer flow, plane jet exhausting into a moving stream, circular jet exhausting into a moving stream, and wall jet flow. Computational results compare favorably with experimental data for most of the examples considered. Significantly improved results were obtained for the plane jet flow, the circular jet flow, and the wall jet flow; whereas the remainder are comparable to those obtained by finite difference methods using the standard kappa-epsilon turbulence model. The latter seems to be promising with further improvement of the expression for the eddy viscosity coefficient.

Kim, Sang-Wook↗

NASA NTRS1996

Effects of Gravity on Sheared Turbulence Laden with Bubbles or Droplets

This is a new project which started in May 1996. The main objective of the experimental/numerical study is to improve the understanding of the physics of two-way coupling between the dispersed phase and turbulence in a prototypical turbulent shear flow - homogeneous shear, laden with small liquid droplets (in gas) or gaseous bubbles (in liquid). The method of direct numerical simulation (DNS) is used to solve the full three-dimensional, time-dependent Navier-Stokes equations including the terms describing the two-way coupling between the dispersed phase and the carrier flow. The results include the temporal evolution of the three-dimensional energy and dissipation spectra and the rate of energy transfer across the energy spectrum to understand the fundamental physics of turbulence modulation, especially the effects of varying the magnitude of gravitational acceleration. The mean-square displacement and diffusivity of the droplets (or bubbles) of a given size and the preferential accumulation of droplets in low vorticity regions and bubbles in high vorticity regions will be examined in detail for different magnitudes of gravitational acceleration. These numerical results which will be compared with their corresponding measured data will provide a data base from which a subgrid-scale (SGS) model can be developed and validated for use in large-eddy simulation (LES) of particle-laden shear flows. Two parallel sets of experiments will be conducted: bubbles in an immiscible liquid and droplets in air. In both experiments homogeneous shear will be imposed on the turbulent carrier flow. The instantaneous velocities of the fluid and polydispersed-size particles (droplets or bubbles) will be measured simultaneously using a two-component Phase-Doppler Particle Analyzer (PDPA). Also, the velocity statistics and energy spectra for the carrier flow will be measured.

Elghobashi, Said↗

NASA NTRS1995

A turbulence module for the NPARC code

A turbulence module is developed for the 2D version of the NPARC code which is currently restricted to planar or axisymmetric flows without swirling. Four turbulence models have been built into the module: Baldwin-Lomax, Chien, Shih-Lumley and CMOTT models. The first is a mixing-length eddy-viscosity model which is mainly used for initialization of computational fields and the last three are the low Reynolds number two-equation models. Unlike chien's model, both the Shih-Lumley and CMOTT models do not involve the dimensionless wall distance y(sup +), an advantage for separated flow calculations. Contrary to the NPARC and most other compressible codes, the non-delta form of transport equations is used which leads to a simpler linearization and is more effective than using the delta form in ensuring the positiveness of the turbulent kinetic energy and its dissipation rate. To reduce numerical diffusion while maintaining necessary stability, a second-order accurate and bounded scheme is used for the convective terms of the turbulent transport equations. This scheme is implemented in a deferred correction manner so that the main coefficients of the resulting difference equations are always positive, thus making the numerical solutions process unconditionally stable. The system of equations is solved via a decoupled method and by the alternating direction TDMA of Thomas. The module can be easily linked to the NPARC code for turbulent flow calculations.

Zhu, J.↗

NASA NTRS1973

A method for calculating unsteady turbulent boundary layers in two- and three-dimensional flows.

The governing equations for an unsteady turbulent boundary layer on a swept infinite cylinder, composed of a continuity equation, a pair of momentum equations and a pair of rate equations for the shear stress, based on the turbulent kinetic-energy equation, are solved numerically. These rate equations for the shear-stress express a balance between the convection, production, dissipation and diffusion of the turbulent shear stress components. Due to the physical model of turbulence employed, this system of equations is hyperbolic. An explicit, second-order accurate, conditionally stable difference scheme for this system, together with appropriate boundary and initial conditions, is formulated and developed into a computer program. Calculations for oscillating free stream flows with no pressure gradient show significant unsteady effects on the turbulent boundary layer.

Singleton, R. E.↗

NASA NTRS1993

A small-scale turbulence model

A previously derived analytical model for the small-scale structure of turbulence is reformulated in such a way that the energy spectrum may be computed. The model is an ensemble of two-dimensional (2D) vortices with internal spiral structure, each stretched by an axially symmetric strain flow. Stretching and differential rotation produce an energy cascade to smaller scales in which the stretching represents the effect of instabilities and the spiral structure is the source of dissipation at the end of the cascade. The energy spectrum of the resulting flow may be expressed as a time integration involving only the enstrophy spectrum of the time evolving 2D cross section flow, which may be obtained numerically. Examples are given in which a k exp -5/3 spectrum is obtained by this method. The k exp -5/3 inertial range spectrum is shown to be related to the existence of a self-similar enstrophy preserving range in the 2D enstrophy spectrum. The results are found to be insensitive to time dependence of the strain rate, including even intermittent on-or-off strains.

Lundgren, T. S.↗

NASA NTRS1993

Role of secondary instability theory and parabolized stability equations in transition modeling

In modeling the laminar-turbulent transition region, the designer depends largely on benchmark data from experiments and/or direct numerical simulations that are usually extremely expensive. An understanding of the evolution of the Reynolds stresses, turbulent kinetic energy, and quantifies in the transport equations like the dissipation and production is essential in the modeling process. The secondary instability theory and the parabolized stability equations method are used to calculate these quantities, which are then compared with corresponding quantities calculated from available direct numerical simulation data for the incompressible boundary-layer flow of laminar-turbulent transition conditions. The potential of the secondary instability theory and the parabolized stability equations approach in predicting these quantities is discussed; results indicate that inexpensive data that are useful for transition modeling in the early stages of the transition region can be provided by these tools.

El-Hady, Nabil M.↗

NASA NTRS1986

A two-dimensional numerical study of the flow inside the combustion chambers of a motored rotary engine

A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.

Shih, T. I. P.↗

NASA NTRS1986

A two-dimensional numerical study of the flow inside the combustion chamber of a motored rotary engine

Shih, T. I-P.↗

NASA NTRS1999

Comparison of AGE and Spectral Methods for the Simulation of Far-Wakes

Turbulent flow simulation methods based on finite differences are attractive for their simplicity, flexibility and efficiency, but not always for accuracy or stability. This report demonstrates that a good compromise is possible with the Advected Grid Explicit (AGE) method. AGE has proven to be both efficient and accurate for simulating turbulent free-shear flows, including planar mixing layers and planar jets. Its efficiency results from its localized fully explicit finite difference formulation (Bisset 1998a,b) that is very straightforward to compute, outweighing the need for a fairly small timestep. Also, most of the successful simulations were slightly under-resolved, and therefore they were, in effect, large-eddy simulations (LES) without a sub-grid-scale (SGS) model, rather than direct numerical simulations (DNS). The principle is that the role of the smallest scales of turbulent motion (when the Reynolds number is not too low) is to dissipate turbulent energy, and therefore they do not have to be simulated when the numerical method is inherently dissipative at its resolution limits. Such simulations are termed 'auto-LES' (LES with automatic SGS modeling) in this report.

Bisset, D. K.↗

NASA NTRS1990

Statistical energy analysis of a geared rotor system

The vibroacoustic response of a generic geared rotor system is analyzed on an order of magnitude basis utilizing an approximate statistical energy analysis method. This model includes a theoretical coupling loss factor for a generic bearing component, which properly accounts for the vibration transmission through rolling element bearing. A simplified model of a NASA test stand that assumes vibratory energy flow from the gear mesh source to the casing through shafts and bearings is given as an example. Effects of dissipation loss factor and gearbox radiation efficiency models are studied by comparing predictions with NASA test results.

Lim, Teik C.↗

NASA NTRS1995

Development of a two-equation turbulence model for hypersonic flows: Evaluation of a low Reynolds number correction to the Kappa - epsilon two equation compressible turbulence model - Volume 1

The objective of the current research is the development of an improved k-epsilon two-equation compressible turbulence model for turbulent boundary layer flows experiencing strong viscous-inviscid interactions. The development of an improved model is important in the design of hypersonic vehicles such as the National Aerospace Plane (NASP) and the High Speed Civil Transport (HSCT). Improvements have been made to the low Reynolds number functions in the eddy viscosity and dissipation of solenoidal dissipation of the k-epsilon turbulence mode. These corrections offer easily applicable modifications that may be utilized for more complex geometries. The low Reynolds number corrections are functions of the turbulent Reynolds number and are therefore independent of the coordinate system. The proposed model offers advantages over some current models which are based upon the physical distance from the wall, that modify the constants of the standard model, or that make more corrections than are necessary to the governing equations. The code has been developed to solve the Favre averaged, boundary layer equations for mass, momentum, energy, turbulence kinetic energy, and dissipation of solenoidal dissipation using Keller's box scheme and the Newton spatial marching method. The code has been validated by removing the turbulent terms and comparing the solution with the Blasius solution, and by comparing the turbulent solution with an existing k-epsilon model code using wall function boundary conditions. Excellent agreement is seen between the computed solution and the Blasius solution, and between the two codes. The model has been tested for both subsonic and supersonic flat-plate turbulent boundary layer flow by comparing the computed skin friction with the Van Driest II theory and the experimental data of Weighardt; by comparing the transformed velocity profile with the data of Weighardt, and the Law of the Wall and the Law of the Wake; and by comparing the computed results of an adverse pressure gradient with the experimental data of Fernando and Smits. Good agreement is obtained with the experimental correlations for all flow conditions.

Knight, Doyle D.↗