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NASA NTRS1991

Turbulence closure modeling near rigid boundaries

The near-wall region plays an essential role in turbulent boundary layers: it is a region of high shear; the peak rate of production and peak intensity of turbulence occurs there; and the peak rate of dissipation occurs right at the wall. Nevertheless, this region has received less attention from modelers than have more nearly homogeneous flows. One reason for this is that when the boundary layer is near equilibrium, experimental data can be used to prescribe the flow in the wall layer. Another reason is that most turbulence models are developed under assumptions of near homogeneity. This is a poor approximation in the wall region. A single-point moment closure model for the strongly non-homogeneous A turbulent flow near a rigid boundary is developed.

Durbin, Paul A.↗
NASA NTRS1991

Modeling hypersonic boundary-layer flows with second-moment closure

An ongoing research effort designed to apply the best possible second-moment-closure model to simulate complex hypersonic flows is presented. The baseline model under consideration is the Launder-Reece-Rodi Reynolds stress transport turbulence model. Two add-ons accounting for wall effects, namely, the Launder-Shima low-Reynolds-number model and the compressible wall-function technique, are tested. Results are reported for flow over a flat plate, both adiabatic-wall and cooled-wall cases. It has been found that further improvements of the existing models are necessary to achieve accurate prediction in high Mach number flow range.

Huang, P. George↗
NASA NTRS1991

Stationary turbulent closure via the Hopf functional equation

Explicit solutions of the stationary Hopf equation are discussed and their computational possibilities are explored. The motivation is to circumvent the infinite hierarchy of coupled equations for the velocity moments and obtain an exact closure of the steady-state 3D Navier-Stokes equations, without modeling assumptions or truncation. The Hopf formulation of the Navier-Stokes equation is reviewed. A stationary homogeneous solution for 2D flow is displayed and discussed. It is shown how depletion of nonlinearity may arise for 3D forced homogeneous flow. The general 3D forced case is considered and a method for closing the 3D unforced equations with arbitrary boundary conditions is derived.

Shen, Hubert H.↗
NASA NTRS1993

Reynolds stress closure modeling in wall-bounded flows

This report describes two projects. Firstly, a Reynolds stress closure for near-wall turbulence is described. It was motivated by the simpler k-epsilon-(v-bar(exp 2)) model described in last year's annual research brief. Direct Numerical Simulation of three-dimensional channel flow shows a curious decrease of the turbulent kinetic energy. The second topic of this report is a model which reproduces this effect. That model is described and used to discuss the relevance of the three dimensional channel flow simulation to swept wing boundary layers.

Durbin, Paul A.↗
NASA NTRS1993

Results of the second Round Robin on opening-load measurement conducted by ASTM Task Group E24.04.04 on crack closure measurement and analysis

A second experimental Round Robin on the measurement of the crack opening load in fatigue crack growth tests has been completed by the ASTM Task Group E24.04.04 on Crack Closure Measurement and Analysis. Fourteen laboratories participated in the testing of aluminum alloy compact tension specimens. Opening-load measurements were made at three crack lengths during constant Delta K, constant stress ratio tests by most of the participants. Four participants made opening-load measurements during threshold tests. All opening-load measurements were based on the analysis of specimens compliance behavior, where the displacement/strain was measured either at the crack mouth or the mid-height back face location. The Round Robin data were analyzed for opening load using two non-subjective analysis methods: the compliance offset and the correlation coefficient methods. The scatter in the opening load results was significantly reduced when some of the results were excluded from the analysis population based on an accept/reject criterion for raw data quality. The compliance offset and correlation coefficient opening load analysis methods produced similar results for data populations that had been screened to eliminate poor quality data.

Phillips, E. P.↗
NASA NTRS1993

A representation for the turbulent mass flux contribution to Reynolds-stress and two-equation closures for compressible turbulence

The turbulent mass flux, or equivalently the fluctuating Favre velocity mean, appears in the first and second moment equations of compressible kappa-epsilon and Reynolds stress closures. Mathematically it is the difference between the unweighted and density-weighted averages of the velocity field and is therefore a measure of the effects of compressibility through variations in density. It appears to be fundamental to an inhomogeneous compressible turbulence, in which it characterizes the effects of the mean density gradients, in the same way the anisotropy tensor characterizes the effects of the mean velocity gradients. An evolution equation for the turbulent mass flux is derived. A truncation of this equation produces an algebraic expression for the mass flux. The mass flux is found to be proportional to the mean density gradients with a tensor eddy-viscosity that depends on both the mean deformation and the Reynolds stresses. The model is tested in a wall bounded DNS at Mach 4.5 with notable results.

Ristorcelli, J. R.↗
NASA NTRS1994

Development of a near-wall Reynolds-stress closure based on the SSG model for the pressure strain

In this research, a near-wall second-order closure based on the Speziable et al.(1991) or SSG model for the pressure-strain term is proposed. Unlike the LRR model, the SSG model is quasi-nonlinear and yields better results when applied to calculate rotating homogeneous turbulent flows. An asymptotic analysis near the wall is applied to both the exact and modeled, equations so that appropriate near-wall corrections to the SSG model and the modeled dissipation-rate equation can be derived to satisfy the physical wall boundary conditions as well as the asymptotic near-wall behavior of the exact equations. Two additional model constants are introduced and they are determined by calibrating against one set of near-wall channel flow data. Once determined, their values are found to remain constant irrespective of the type of flow examined. The resultant model is used to calculate simple turbulent flows, near separating turbulent flows, complex turbulent flows and compressible turbulent flows with a freestream Mach number as high as 10. In all the flow cases investigated, the calculated results are in good agreement with data. This new near-wall model is less ad hoc, physically and mathematically more sound and eliminates the empiricism introduced by Zhang. Therefore, it is quite general, as demonstrated by the good agreement achieved with measurements covering a wide range of Reynolds numbers and Mach numbers.

So, R. M. C.↗
NASA NTRS1994

The application of Newman crack-closure model to predicting fatigue crack growth

Newman crack-closure model and the relevant crack growth program were applied to the analysis of crack growth under constant amplitude and aircraft spectrum loading on a number of aluminum alloy materials. The analysis was performed for available test data of 2219-T851, 2024-T3, 2024-T351, 7075-T651, 2324-T39, and 7150-T651 aluminum materials. The results showed that the constraint factor is a significant factor in the method. The determination of the constraint factor is discussed. For constant amplitude loading, satisfactory crack growth lives could be predicted. For the above aluminum specimens, the ratio of predicted to experimental lives, Np/Nt, ranged from 0.74 to 1.36. The mean value of Np/Nt was 0.97. For a specified complex spectrum loading, predicted crack growth lives are not in very good agreement with the test data. Further effort is needed to correctly simulate the transition between plane strain and plane stress conditions, existing near the crack tip.

Si, Erjian↗
NASA NTRS1994

Modeling near wall effects in second moment closures by elliptic relaxation

The elliptic relaxation model of Durbin (1993) for modeling near-wall turbulence using second moment closures (SMC) is compared to DNS data for a channel flow at Re(sub t) = 395. The agreement for second order statistics and even the terms in their balance equation is quite satisfactory, confirming that very little viscous effects (via Kolmogoroff scales) need to be added to the high Reynolds versions of SMC for near-wall-turbulence. The essential near-wall feature is thus the kinematic blocking effect that a solid wall exerts on the turbulence through the fluctuating pressure, which is best modeled by an elliptic operator. Above the transition layer, the effect of the original elliptic operator decays rapidly, and it is suggested that the log-layer is better reproduced by adding a non-homogeneous reduction of the return to isotropy, the gradient of the turbulent length scale being used as a measure of the inhomogeneity of the log-layer. The elliptic operator was quite easily applied to the non-linear Craft & Launder pressure-strain model yielding an improved distinction between the spanwise and wall normal stresses, although at higher Reynolds number (Re) and away from the wall, the streamwise component is severely underpredicted, as well as the transition in the mean velocity from the log to the wake profiles. In this area a significant change of behavior was observed in the DNS pressure-strain term, entirely ignored in the models.

Laurence, D.↗
NASA NTRS1995

Classical closure theory and Lam's interpretation of epsilon-RNG

Lam's phenomenological epsilon-renormalization group (RNG) model is quite different from the other members of that group. It does not make use of the correspondence principle and the epsilon-expansion procedure. We demonstrate that Lam's epsilon-RNG model is essentially the physical space version of the classical closure theory in spectral space and consider the corresponding treatment of the eddy viscosity and energy backscatter.

Zhou, YE↗
NASA NTRS1994

Roles of drizzle in a one-dimensional third-order turbulence closure model of the nocturnal stratus-topped marine boundary layer

This study focuses on the effects of drizzle in a one-dimensional third-order turbulence closure model of the nocturnal stratus-topped marine boundary layer. When the simulated drizzle rate is relatively small (maximum approximately equal to 0.6 mm/day), steady-state solutions are obtained. The boundary layer stabilizes essentially because drizzle causes evaporative cooling of the subcloud layer. This stabilization considerably reduces the buoyancy flux and turbulence kinetic energy below the stratus cloud. Thus, drizzle tends to decouple the cloud from the subcloud layer in the model, as suggested by many observational studies. In addition, the evaporation of drizzle in the subcloud layer creates small scattered clouds, which are likely to represent cumulus clouds, below the solid stratus cloud in the model. The sensitivity experiments show that these scattered clouds help maintain a coupled boundary layer. When the drizzle rate is relatively large (maximum approximately equal to 0.9 mm/day), the response of the model becomes transient with bursts in turbulent fluxes. This phenomenon is related to the formation of the scattered cloud layer below the solid stratus cloud. It appears that the model is inadequate to represent the heat and moisture transport by strong updrafts covering a small fractional area in cumulus convection.

Wang, Shouping↗
NASA NTRS1995

A new approach to the formulation of scalar flux closure

This report shows that if a stochastic differential equation (Langevin equation) for velocity fluctuation vector is known, it is possible to derive the equations for scalar flux transport. Durbin and Speziale (1994) showed that the second moment of this stochastic differential equation gives an equation for the evolution of Reynolds stress tensor. Similarly, the stochastic equation will give an equation for scalar flux. Therefore, a coupling between these two is present. The basis for the present work is that there should be Langevin equations that can produce acceptable models for both the Reynolds stress tensor and the scalar flux vector. Having found this basic Langevin equation, the amount of work needed to model the second order closure problems is reduced; using the well developed models for Reynolds stress equations, it will be possible to derive corresponding models for scalar flux equation.

Shabany, Y.↗
NASA NTRS1996

Second moment closure analysis of the backstep flow database

A Second Moment Closure computation (SMC) is compared in detail with the Direct Numerical Simulation (DNS) data of Le and Moin for the backstep flow at Re = 5,000 in an attempt to understand why the intensity of the backflow and, consequently, the friction coefficient in the recirculation bubble are severely underestimated. The data show that this recirculation bubble is far from being laminar except in the very near wall layer. A novel 'differential a priori' procedure was used, in which the full transport equation for one isolated component of the Reynolds stress tensor was solved using DNS data as input. Conclusions are then different from what would have been deduced by comparing a full simulation to a DNS. One cause of discrepancy was traced back to insufficient transfer of energy to the normal stress by pressure strain, but was not cured. A significant finding, confirmed by the DNS data in the core region of a channel flow, is that the coefficient that controls destruction of dissipation, C epsilon(sub 2), should be decreased by a factor of 2 when production is vanishing. This is also the case in the recirculation bubble, and a new formulation has cured 25% of the backflow discrepancy.

Parneix, S.↗
NASA NTRS1998

Some Results Relevant to Statistical Closures for Compressible Turbulence

For weakly compressible turbulent fluctuations there exists a small parameter, the square of the fluctuating Mach number, that allows an investigation using a perturbative treatment. The consequences of such a perturbative analysis in three different subject areas are described: 1) initial conditions in direct numerical simulations, 2) an explanation for the oscillations seen in the compressible pressure in the direct numerical simulations of homogeneous shear, and 3) for turbulence closures accounting for the compressibility of velocity fluctuations. Initial conditions consistent with small turbulent Mach number asymptotics are constructed. The importance of consistent initial conditions in the direct numerical simulation of compressible turbulence is dramatically illustrated: spurious oscillations associated with inconsistent initial conditions are avoided, and the fluctuating dilatational field is some two orders of magnitude smaller for a compressible isotropic turbulence. For the isotropic decay it is shown that the choice of initial conditions can change the scaling law for the compressible dissipation. A two-time expansion of the Navier-Stokes equations is used to distinguish compressible acoustic and compressible advective modes. A simple conceptual model for weakly compressible turbulence - a forced linear oscillator is described. It is shown that the evolution equations for the compressible portions of turbulence can be understood as a forced wave equation with refraction. Acoustic modes of the flow can be amplified by refraction and are able to manifest themselves in large fluctuations of the compressible pressure.

Ristorcelli, J. R.↗
NASA NTRS1997

Prediction and measurement of direct-normal solar irradiance: A closure experiment

Direct-Normal Solar Irradiance (DNSI), the total energy in the solar spectrum incident on a plane perpendicular to the Sun's direction on a unit area at the earth's surface in unit time, depends only on the atmospheric extinction of sunlight without regard to the details of extinction-whether absorption or scattering. Here the authors describe a set of closure experiments performed in north-central Oklahoma, wherein measured atmospheric composition is input to a radiative transfer model, MODTRAN-3, to predict DNSI, which is then compared to measured values. Thirty six independent comparisons are presented; the agreement between predicted and measured values falls within the combined uncertainties in the prediction (2%) and measurement (0.2%) albeit with a slight bias ((approximately) 1% overprediction) that is independent of the solar zenith angle. Thus these results establish the adequacy of current knowledge of the solar spectrum and atmospheric extinction as embodied in MODTRAN-3 for use in climate models. An important consequence is the overwhelming likelihood that the atmospheric clear-sky absorption is accurately described to within comparable uncertainties.

Halthore, R. N.↗
NASA NTRS1999

Ocean Turbulence: One-Point Closure Model Momentum, Heat and Salt Vertical Diffusivities in the Presence of Shear - Paper 2

We develop and test a 1-point closure turbulence model with the following features: 1) we include the salinity field and derive the expression for the vertical turbulent diffusivities of momentum K(sub m) , heat K(sub h) and salt K(sub s) as a function of two stability parameters: the Richardson number R(sub i) (stratification vs. shear) and the Turner number R(sub rho) (salinity gradient vs. temperature gradient). 2) to describe turbulent mixing below the mixed layer (ML), all previous models have adopted three adjustable "background diffusivities" for momentum, heat and salt. We propose a model that avoids such adjustable diffusivities. We assume that below the ML, the three diffusivities have the same functional dependence on R( sub i) and R(sub rho) as derived from the turbulence model. However, in order to compute R(sub i) below the ML, we use data of vertical shear due to wave-breaking.measured by Gargett et al. The procedure frees the model from adjustable background diffusivities and indeed we employ the same model throughout the entire vertical extent of the ocean. 3) in the local model, the turbulent diffusivities K(sub m,h,s) are given as analytical functions of R(sub i) and R(sub rho). 5) the model is used in an O-GCM and several results are presented to exhibit the effect of double diffusion processes. 6) the code is available upon request.

Canuto, V. M.↗
NASA NTRS1999

STS-103 Payload Door Closure: Hubble Repair. Discovery

Live footage of the Discovery's cargo bay door closure is shown. Discovery's payload include an Orbital Replacement Unit Carrier that contains the tools and replacement parts necessary to service the HST and Flight Support System that will hold the telescope during servicing.

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