Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “dissipation rate”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Energetics of global ocean tides from Geosat altimetry

The present paper focuses on resonance and energetics of the daily tides, especially in the southern ocean, the distribution of gravitational power input of daily and half-daily tides, and comparison with other estimates of global dissipation rates. The present global tidal maps, derived from Geosat altimetry, compare favorably with ground truth data at about the same rms level as the models of Schwiderski (1983), and are slightly better in lunar than in solar tides. Diurnal admittances clearly show Kelvin wave structure in the southern ocean and confirm the resonant mode of Platzman (1984) at 28.5 + or - 0.1 hr with an apparent Q of about 4. Driving energy is found to enter dominantly in the North Pacific for the daily tides and is strongly peaked in the tropical oceans for the half-daily tides. Global rates of working on all major tide constituents except S2 agree well with independent results from analyses of gravity through satellite tracking. Comparison at S2 is improved by allowing for the air tide in gravitational results but suggests deficiencies in all solar tide models.

Cartwright, David E.↗
NASA NTRS1991

Electrical energy sources for organic synthesis on the early earth

It is pointed out that much of the contemporary origin-of-life research uses the original estimates of Miller and Urey (1959) for terrestrial energy dissipation by lightning and coronal discharges being equal to 2 x 10 to the 19th J/yr and 6 x 10 to the 19th J/yr, respectively. However, data from experiments that provide analogues to naturally-occurring lightning and coronal discharges indicate that lightning energy yields for organic synthesis (nmole/J) are about one order of magnitude higher than the coronal discharge yields. This suggests that, on early earth, organic production by lightning may have dominated that due to coronal emission. New values are recommended for lightning and coronal discharge dissipation rates on the early earth, 1 x 10 to the 18th J/yr and 5 x 10 to the 17th J/yr, respectively.

Chyba, Christopher↗
NASA NTRS1991

A critical comparison of second order closures with direct numerical simulation of homogeneous turbulence

Recently, several second order closure models have been proposed for closing the second moment equations, in which the velocity-pressure gradient (and scalar-pressure gradient) tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behavior in different flows have not been fully examined because they are un-measurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the opportunity to do this kind of study. With the direct numerical simulation, we may use the solution to exactly calculate the values of these correlation terms and then directly compare them with the values from their modeled formulations (models). Here, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of forty five homogeneous flows which were done by Rogers et al. (1986) and Lee et al. (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones which give the best performance. The modeling procedure, model constraints, and the various evaluated models are described. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.

Shih, Tsan-Hsing↗
NASA NTRS1991

Advancements in engineering turbulence modeling

Some new developments in two-equation models and second order closure models are presented. Two-equation models (k-epsilon models) have been widely used in computational fluid dynamics (CFD) for engineering problems. Most of low-Reynolds number two-equation models contain some wall-distance damping functions to account for the effect of wall on turbulence. However, this often causes the confusion and difficulties in computing flows with complex geometry and also needs an ad hoc treatment near the separation and reattachment points. A set of modified two-equation models is proposed to remove the aforementioned shortcomings. The calculations using various two-equation models are compared with direct numerical simulations of channel flow and flat boundary layers. Development of a second order closure model is also discussed with emphasis on the modeling of pressure related correlation terms and dissipation rates in the second moment equations. All the existing models poorly predict the normal stresses near the wall and fail to predict the 3-D effect of mean flow on the turbulence (e.g. decrease in the shear stress caused by the cross flow in the boundary layer). The newly developed second order near-wall turbulence model is described and is capable of capturing the near-wall behavior of turbulence as well as the effect of 3-D mean flow on the turbulence.

Shih, T.-H.↗
NASA NTRS1992

A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models

This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.

Navier-Stoke solver↗
NASA NTRS1992

Advances in engineering turbulence modeling

Some new developments in two equation models and second order closure models are presented. In this paper, modified two equation models are proposed to remove shortcomings such as computing flows over complex geometries and the ad hoc treatment near the separation and reattachment points. The calculations using various two equation models are compared with direct numerical solutions of channel flows and flat plate boundary layers. Development of second order closure models will also be discussed with emphasis on the modeling of pressure related correlation terms and dissipation rates in the second moment equations. All existing models poorly predict the normal stresses near the wall and fail to predict the three dimensional effect of mean flow on the turbulence. The newly developed second order near-wall turbulence model to be described in this paper is capable of capturing the near-wall behavior of turbulence as well as the effect of three dimension mean flow on the turbulence.

Shih, T.-H.↗
NASA NTRS1992

An experimental investigation of the separating/reattaching flow over a backstep

Transport characteristics of the turbulent kinetic energy, k, and the shear stream, bar(-uv), were studied in an incompressible boundary layer downstream of the reattachment of the separated flow behind a backward facing step. Hot-wire measurement techniques were used to measure three Reynolds stresses and higher order mean products of velocity fluctuations. These quantities were used to evaluate advection, turbulent diffusion, and production terms of the k and bar(-uv) transport equations. The dissipation rate and pressure-strain terms were obtained as the difference of all the other terms. The Reynolds number based on the step height was 37,000 and the upstream oncoming flow was fully developed turbulent boundary layer with the R(sub theta) = 3600.

Jovic, Srboljub↗
NASA NTRS1992

Low Reynolds number multiple-time-scale turbulence model and calculations of steady and pulsating shear layers

A low Reynolds number multiple-time-scale turbulence model (LMS) and its application to fully developed turbulent channel flows and pulsating pipe flows are presented. The LMS can describe the inequilibrium turbulence phenomena down to the viscous sublayer. The calculated fluid flow and turbulence fields for the channel flows are in better agreement with the direct numerical simulation (DNS) results than those obtained using a Reynolds stress turbulence model, and the calculated near-wall dissipation rates are in qualitatively correct agreement with the DNS results. The LMS also successfully predicts the rapidly varying phase-lead of the wall shearing stress that occurs in a narrow range of the dimensionless frequency omega (+) = (omega x nu)/(upsilon x tau(exp2)) for the pulsating pipe flows while various other turbulence models fail to predict this phenomenon, and the LMS yields significantly improved numerical results for a wide range of the dimensionless frequency compared with those obtained using a rapid distortion theory (RDT).

Kim, Sang-Wook↗
NASA NTRS1990

One-equation near-wall turbulence modeling with the aid of direct simulation data

The length scales appearing in the relations for the eddy viscosity and dissipation rate in one-equation models were evaluated from direct numerical simulation data for developed channel and boundary-layer flow at two Reynolds numbers each. To prepare the ground for the evaluation, the distribution of the most relevant mean-flow and turbulence quantities is presented and discussed with respect to Reynolds-number influence and to differences between channel and boundary-layer flow. An alternative model is also examined in which bar-(v'(exp 2))(exp 1/2) is used as velocity scale instead of k(exp 1/2). With this velocity scale, the length scales now appearing in the model follow very closely a linear relationship near the wall so that no damping is necessary. For the determination of bar-v'(exp 2) in the context of a one-equation model, a correlation is provided between bar-(v'(exp 2))/k and bar-(u'v')/k.

Rodi, W.↗
NASA NTRS1991

Nonlinear magnetohydrodynamics by Galerkin-method computation

A fully spectral numerical code is used to explore the properties of voltage-driven dissipative magnetofluids inside a periodic cylinder with circular cross section. The trial functions are orthonormal eigenfunctions of the curl (Chandrasekhar-Kendall functions). Transitions are observed from axisymmetric resistive equilibria without flow to helically deformed laminar states with flow, and between pairs of helical laminar states with different pairs of poloidal and toroidal m and n numbers. States of minimum energy dissipation rate seem to be preferred. At high values of the pinch ratio, fully developed magnetohydrodynamic turbulence is observed.

Shan, Xiaowen↗
NASA NTRS1992

Probability density functions in turbulent channel flow

The probability density functions (pdf's) of the fluctuating velocity components, as well as their first and second derivatives, are calculated using data from the direct numerical simulations (DNS) of fully developed turbulent channel flow. It is observed that, beyond the buffer region, the pdf of each of these quantities is independent of the distance from the channel wall. It is further observed that, beyond the buffer region, the pdf's for all the first derivatives collapse onto a single universal curve and those of the second derivatives also collapse onto another universal curve, irrespective of the distance from the wall. The kinetic-energy dissipation rate exhibits log normal behavior.

Dinavahi, Surya P. G.↗
NASA NTRS1993

Fuel injector: Air swirl characterization aerothermal modeling, phase 2, volume 1

A well integrated experimental/analytical investigation was conducted to provide benchmark quality relevant to a prefilming type airblast fuel nozzle and its interaction with the combustor dome air swirler. The experimental investigation included a systematic study of both single-phase flows that involved single and twin co-axial jets with and without swirl. A two-component Phase Doppler Particle Analyzer (PDPA) was used to document the interaction of single and co-axial air jets with glass beads that simulate nonevaporating spray and simultaneously avoid the complexities associated with fuel atomization processes and attendant issues about the specification of relevant boundary conditions. The interaction of jets with methanol spray produced by practical airblast nozzle was also documented in the spatial domain of practical interest. Model assessment activities included the use of three turbulence models (k-epsilon, algebraic second moment (ASM), and differential second moment (DSM)) for the carrier phase, deterministic or stochastic Lagrangian treatment of the dispersed phase, and advanced numerical schemes. Although qualitatively good comparison with data was obtained for most of the cases investigated, the model deficiencies in regard to modeled dissipation rate transport equation, single length scale, pressure-strain correlation, and other critical closure issues need to be resolved before one can achieve the degree of accuracy required to analytically design combustion systems.

Nikjooy, M.↗
NASA NTRS1993

Fuel Injector: Air swirl characterization aerothermal modeling, phase 2, volume 2

A well integrated experimental/analytical investigation was conducted to provide benchmark quality data relevant to prefilming type airblast fuel nozzle and its interaction with combustor dome air swirler. The experimental investigation included a systematic study of both single-phase flows that involved single and twin co-axial jets with and without swirl. A two-component Phase Doppler Particle Analyzer (PDPA) equipment was used to document the interaction of single and co-axial air jets with glass beads that simulate nonevaporating spray and simultaneously avoid the complexities associated with fuel atomization processes and attendant issues about the specification of relevant boundary conditions. The interaction of jets with methanol spray produced by practical airblast nozzle was also documented in the spatial domain of practical interest. Model assessment activities included the use of three turbulence models (k-epsilon, algebraic second moment (ASM) and differential second moment (DSM)) for the carrier phase, deterministic or stochastic Lagrangian treatment of the dispersed phase, and advanced numerical schemes. Although qualitatively good comparison with data was obtained for most of the cases investigated, the model deficiencies in regard to modeled dissipation rate transport equation, single length scale, pressure-strain correlation, and other critical closure issues need to be resolved before one can achieve the degree of accuracy required to analytically design combustion systems.

Nikjooy, M.↗
NASA NTRS1993

On the assumption of vanishing temperature fluctuations at the wall for heat transfer modeling

Boundary conditions for fluctuating wall temperature are required for near-wall heat transfer modeling. However, their correct specifications for arbitrary thermal boundary conditions are not clear. The conventional approach is to assume zero fluctuating wall temperature or zero gradient for the temperature variance at the wall. These are idealized specifications and the latter condition could lead to an ill posed problem for fully-developed pipe and channel flows. In this paper, the validity and extent of the zero fluctuating wall temperature condition for heat transfer calculations is examined. The approach taken is to assume a Taylor expansion in the wall normal coordinate for the fluctuating temperature that is general enough to account for both zero and non-zero value at the wall. Turbulent conductivity is calculated from the temperature variance and its dissipation rate. Heat transfer calculations assuming both zero and non-zero fluctuating wall temperature reveal that the zero fluctuating wall temperature assumption is in general valid. The effects of non-zero fluctuating wall temperature are limited only to a very small region near the wall.

Sommer, T. P.↗
NASA NTRS1992

A near-wall two-equation model for turbulent heat fluxes

A near-wall two-equation model for turbulent heat fluxes is derived from the temperature variance and its dissipation-rate equations and the assumption of gradient transport. Only incompressible flows with non-buoyant heat transfer are considered. The near-wall asymptotics of each term in the exact equations are examined and used to derive near-wall correction functions that render the modeled equations consistent with these behavior. Thus modeled, the equations are used to calculate fully-developed pipe and channel flows with heat transfer. It is found that the proposed two-equation model yields asymptotically correct near-wall behavior for the normal heat flux, the temperature variance and its near-wall budget and correct limiting wall values for these properties compared to direct simulation data and measurements obtained under different wall boundary conditions.

Sommer, T. P.↗
NASA NTRS1993

A simplified Reynolds stress model for unsteady turbulent boundary layers

A simplified Reynolds stress model has been developed for the prediction of unsteady turbulent boundary layers. By assuming that the net transport of Reynolds stresses is locally proportional to the net transport of the turbulent kinetic energy, the time dependent full Reynolds stress model is reduced to a set of ordinary differential equations. These equations contain only time derivatives and can be readily integrated in a time dependent boundary layer or Navier-Stokes code. The turbulent kinetic energy and dissipation rate needed for the model are obtained by solving the k-epsilon equations. This simplified Reynolds stress turbulence model (SRSM) does not use the eddy viscosity assumption, which may not be valid for unsteady turbulent flows. The anisotropy of both the steady and the unsteady turbulent normal stresses can be captured by the SRSM model. Through proper damping of the shear stresses, the present model can be used in the near wall region of turbulent boundary layers. This model has been validated against data for steady and unsteady turbulent boundary layers, including periodic turbulent boundary layers subjected to a mean adverse pressure gradient. For the cases tested, the predicted unsteady velocity and turbulent stress components agree well with the experimental data. Comparison between the predictions from the SRSM model and a k-epsilon model is also presented.

Fan, Sixin↗
NASA NTRS1993

Critical comparison of second-order closures with direct numerical simulations of homogeneous turbulence

Recently, several models have been proposed for closing the second-moment equations, in which the velocity-pressure gradient tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so-called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behaviors in different flows have not been fully examined because they are unmeasurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the possibility to do this kind of study. With direct numerical simulation, we may use the solution to calculate exactly the values of these correlation terms and then directly compare them with the values from their modeled formulations. In this paper, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of 45 homogeneous flows, which were done by Rogers et al. (1986) and Lee and Reynolds (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones that give the best performance. The paper also describes the modeling procedure, model constraints, and the various evaluated models. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.

Shih, Tsan-Hsing↗
NASA NTRS1993

Experimental and numerical study of a turbulent boundary layer with pressure gradients

Results are presented of an experimental and numerical study of a turbulent boundary layer with pressure gradients conducted using the recent 'fringe method' with its numerical advantages and good inflow quality. After an inflow transient good agreement is observed; the differences, of up to 13 percent, are discussed. Moderate deviations from the law of the wall are found in the velocity profiles of the simulation. They are fully correlated with the pressure gradient, are in fair quantitative agreement with the experimental results of Nagano et al. (1992), and are roughly the opposite of uncorrected mixing-length-model predictions. Large deviations from the wall scaling are observed for other quantities, notably for the turbulence dissipation rate. The a(1) structure parameter drops mildly in the upper layer with adverse pressure gradient.

Spalart, Philippe R.↗