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For homogeneous flows the rapid pressure-strain correlation tensor can be written in terms of the mean velocity gradient and an integral of the two-point correlation tensor. In the present study the two-point correlation tensor is modeled and analytically integrated to obtain the pressure-strain model coefficients, which can then be expressed in terms of closed integrals of the two-point correlation model coefficients. Therefore, deficiencies of the pressure-strain models can be detected and resolved on the two-point correlation level. As an example for the new approach, direct numerical simulations results for a homogeneous shear flow are analyzed in detail and the resulting coefficients are compared to existing model coefficients for linear and nonlinear pressure-strain models.

A nonlinear stress–strain model, derived from the modeled Reynolds stress transport equation, is modified to account for the near wall effects in wall-bounded turbulent flows. Since it is known that wall reflection of the turbulent pressure field modifies the pressure–strain correlation, the approach taken is to introduce a correction to the coefficients in the closure for the pressure–strain correlation purely based on ideas for full Reynolds stress closures. The stress–strain relation is implemented in the context of the k – ϵ model with a variable C μ . Results are presented for plane channel flow and both zero and adverse pressure gradient boundary layers. Favorable results for the anisotropies in the Reynolds stresses are obtained by the new model as validated by comparisons against direct numerical simulation (DNS) and experimental data.

The experimental budgets for the transport equations for heat flux and Reynolds stress are presented for a round turbulent buoyant plume. The pressure correlation terms are deduced as the closing terms and are found to constitute a substantial part of these budgets. Even though a buoyant plume is initiated by buoyancy, it is found that the production of heat flux and Reynolds stress is largely maintained by the mean flow gradients, because the buoyancy production terms are not as large. The results are used to assess the local equilibrium assumption, which implies that the production and destruction terms of the transport equations balance each other. The results are also used to investigate why the mechanical to thermal time scale ratio for a buoyant plume is different than the commonly used value. Finally, some simpler models for the pressure correlation terms, which appear in the heat flux and the Reynolds stress equations, are assessed against those deduced from the experiment.

A closure for the compressible portion of the pressure-strain covariance is developed. It is shown that, within the context of a pressure-strain closure assumption linear in the Reynolds stresses, an expression for the pressure-dilatation can be used to construct a representation for the pressure-strain. Additional closures for the unclosed terms in the Favre–Reynolds stress equations involving the mean acceleration are also constructed. The closures accommodate compressibility corrections depending on the magnitude of the turbulent Mach number, the mean density gradient, the mean pressure gradient, the mean dilatation, and, of course, the mean velocity gradients. The effects of the compressibility corrections on the Favre–Reynolds stresses are consistent with current DNS results. Using the compressible pressure-strain and mean acceleration closures in the Favre–Reynolds stress equations an algebraic closure for the Favre–Reynolds stresses is constructed. Noteworthy is the fact that, in the absence of mean velocity gradients, the mean density gradient produces Favre–Reynolds stresses in accelerating mean flows. Computations of the mixing layer using the compressible closures developed are described. Favre–Reynolds stress closure and two-equation algebraic models are compared to laboratory data for the mixing layer. Experimental data from diverse laboratories for the Favre–Reynolds stresses appears inconsistent and, as a consequence, comparison of the Reynolds stress predictions to the data is not conclusive. Reductions of the kinetic energy and the spread rate are consistent with the sizable decreases seen in these classes of flows.

Direct numerical simulation (DNS) is conducted of a homogeneous turbulent shear flow laden with mono-size particles. The dispersed phase is simulated in the Lagrangian frame and the carrier phase is considered in the Eulerian manner. The coupling between the two phases is `two-way' which allows investigation of the effects of the mass loading ratio and the particle time constant on both phases. A new Reynolds stress model (RSM) is developed based on a `two-fluid' methodology in which both the carrier phase and the dispersed phase are considered in the Eulerian frame. Closures are suggested for the unclosed terms (including the pressure–velocity gradient) which manifest the effects of two-way coupling. The results generated by DNS are used to determine the magnitudes of some of the empirical constants appearing in RSM. The final model predictions for all the components of the fluid, the particle, and fluid-particle Reynolds stresses are assessed via detailed comparisons against DNS data.

A nonlinear stress-strain relation (NLSM) for the turbulence stresses is applied to axisymmetric free shear flows with and without swirl. This relation is an explicit solution to an algebraic Reynolds stress model (ARSIVI). The stress relation is a finite sum of tensor groups depicting various interactions between the mean strain and vorticity fields. Implementation is in the context of a k −e type model. Comparisons are made between flow field predictions obtained with the full Reynolds stress model, the NLSM corresponding to improved and standard ARSMs, the k −e model and experimental data.

In this paper, we present our design of a shrouded probe for high velocity airborne aerosol sampling of particles in the size range 0.1–15 μm diameter. We address many of the problems associated with traditional samplers and discuss the use of a shrouded sampling probe, designed with the aid of computational fluid dynamics, to solve these problems. Techniques for solving the equations governing the fluid motion and individual particle motions are discussed, and the aspiration efficiency of the sampler is calculated. We verify our computational procedures by calculating the airflow and aspiration efficiency of the shrouded probe recently used by McFarland et al. (1989, Environ. Sci. Technol. 23, 1487–1492). The final design includes an evaluation of different inlet tip contours and shroud diameters and their effects on the flow characteristics near the probe inlet, as well as the results of placing a second shroud around the probe to further reduce the velocity of the airflow near the probe inlet. We conclude by presenting a calibration curve for our sampler which can be used to reconstruct freestream particle concentrations and size distributions based on measurements with the sampler.

Experimental data of Hussein et al. (1993) for the turbulent round jet are used to evaluate individual components of Reynolds stress turbulence models. Models for terms in the Reynolds stress equations are reviewed, with particular emphasis on linear and nonlinear pressure-strain models. Improved coefficients for the Choi and Lumley return-to-isotropy expressions have been developed by the authors. These coefficients are valid for a wider range of flows than the currently used coefficients. Pressure-strain and transport model components are compared to the experimental data for the jet, and agreement is very good, indicating that the models are reasonably correct. Predictions using the linear models are generally as good as those obtained using nonlinear models, indicating that nonlinear models may not be necessary for engineering accuracy for this flow.

An asymmetric stent with low porosity patch across the intracranial aneurysm neck and high porosity elsewhere is designed to modify the flow to result in thrombogenesis and occlusion of the aneurysm and yet to reduce the possibility of also occluding adjacent perforator vessels. The purposes of this study are to evaluate the flow field induced by an asymmetric stent using both numerical and digital subtraction angiography (DSA) methods and to quantify the flow dynamics of an asymmetric stent in an in vivo aneurysm model. We created a vein-pouch aneurysm model on the canine carotid artery. An asymmetric stent was implanted at the aneurysm, with 25% porosity across the aneurysm neck and 80% porosity elsewhere. The aneurysm geometry, before and after stent implantation, was acquired using cone beam CT and reconstructed for computational fluid dynamics (CFD) analysis. Both steady-state and pulsatile flow conditions using the measured waveforms from the aneurysm model were studied. To reduce computational costs, we modeled the asymmetric stent effect by specifying a pressure drop over the layer across the aneurysm orifice where the low porosity patch was located. From the CFD results, we found the asymmetric stent reduced the inflow into the aneurysm by 51%, and appeared to create a stasis-like environment which favors thrombus formation. The DSA sequences also showed substantial flow reduction into the aneurysm. Asymmetric stents may be a viable image guided intervention for treating intracranial aneurysms with desired flow modification features.

An improved algebraic Reynolds stress model is developed from the modeled dynamic equations for the Reynolds stress. The improved model more closely represents the original Reynolds stress model equation than the standard algebraic Reynolds stress model over the range of time scales for the turbulence and mean flow strain field. Quasi‐non‐local convective effects are also included in the formulation. Explicit solutions to the algebraic Reynolds stress model equation set, in the form of nonlinear stress‐strain models, are presented for two and three dimensions.

A theoretical study was conducted to determine the effects of adverse pressure gradient and compressibility in modeling turbulent compressible flows. The zero equation, kinetic-energy/dissipation eddy-viscosity models, and Reynolds stress model predictions are presented and compared with experimental data. It is shown that the effects of compressibility, which include the mass-averaged fluctuation term u j '', the pressure-dilatation term p'∂u l ''/∂x l , and the dilatation dissipation μ(∂u l ''/∂x l ) 2 /p, are important in modeling turbulent compressible flows

The unique problems confronting turbulence modelers and experimenters who wish to directly test closure hypotheses are reviewed. Particular attention is paid to the problems presented by systematic errors in the experimental data. Some of the sources of these errors in thermal and laser-Doppler anemometry techniques for measurement are also reviewed, as are problems common to all techniques. The discussion is illustrated by examples from the authors' own work in axisymmetric jets.

This paper discusses the computation of turbulent backstep flow, focusing on the use of Reynolds stress models. A review of existing backstep calculations shows that these calculations generally underpredict reattachment length, and some calculations produce physically unrealistic behavior. Some of these problems are shown to be related to the commonly used pressure-strain coefficients, particularly the linear return-to-isotropy coefficient, C 1 . A new expression for C 1 that is consistent with both homogeneous shear flow experiments and return-to-isotropy experiments produces reasonable results in the present backstep calculations. Some of the present backstep calculations result in unsteady periodic vortex shedding consistent with experimental evidence. This presents a dilemma in the context of Reynolds averaging, which is discussed.

Radial fans of the squirrel-cage type are used in various industrial applications. The analysis of such fans via computational fluid mechanics can provide the overall fan performance coefficients, as well as give insights into the detailed flow field. However, a transient simulation of a 3D machine using a sliding grid for the rotating blades still requires prohibitively large computational resources, with CPU run times in the order of months. To avoid such long simulation times, a faster method is developed in this paper. Instead of solving the transient Navier–Stokes equations, they are first averaged over one impeller rotation, and then solved for the mean flow since only this flow is of practical interest. Due to the averaging process, the blades disappear as solid boundaries, but additional equation terms arise, which represent the blade forces on the fluid. An innovative closure model for these terms is developed by calculating forces in 2D blade rows with the same blade geometry as the 3D machine for a range of flow parameters. These forces are then applied in the 3D machine, and the resulting 3D time-averaged flow field and performance coefficients are calculated. The 3D flow field showed several characteristic features of squirrel-cage blowers, such as a cross-flow pattern through the fan at low flow coefficients, and a vortexlike flow pattern at the fan outlet. The 3D fan performance coefficients showed an excellent agreement with experimental data. Since the 3D simulation solves for the mean flow, it can be run as a steady-state problem with a comparatively coarse grid in the blade region, reducing CPU times by a factor of about 10 when compared to a transient simulation with a sliding grid. It is hoped that these savings in computational cost will encourage other researchers and industrial companies to adopt the new method presented here.

The asymmetric vascular stent (AVS) is a new minimally invasive endovascular device, designed to reduce the potential for further growth and rupture of cerebral aneurysms by substantially modifying the aneurysmal inflow. The low porosity part of the AVS or patch must be deployed to either completely or partially cover the aneurysm orifice. In this study, we investigated the effect on aneurysm hemodynamics of partial coverage with an asymmetric stent using Computational Fluid Dynamics (CFD) analysis and visualization. The low porosity patch of an asymmetric stent was computationally created and deformed to fit into the vessel lumen. Such a patch was placed both in an idealized aneurysm model and in a patient-specific aneurysm model to cover only a portion of the aneurysm orifice either proximally or distally according to the flow direction. The CFD-generated hemodynamic image sequences in the untreated and stented aneurysm models were compared. The asymmetric stent effectively attenuated the aneurysmal flow when the primary inflow was blocked by the patch. Consequently, the Wall Shear Stress (WSS) was reduced, and flow stasis was substantially increased by stenting. For the idealized model, distal placement was better for reducing the inflow jet, whereas for the patient-specific model proximal placement was better. We can conclude that CFD visualizations may be essential to guide either the optimal positioning of a small low porosity region of the AVS or the acceptability of inaccurate placement of a larger AVS patch for partial aneurysm orifice coverage.

There is a general lack of quantitative understanding about how specific design features of endovascular stents (struts and mesh design, porosity) affect the hemodynamics in intracranial aneurysms. To shed light on this issue, we studied two commercial high-porosity stents (Tristar stent™ and Wallstent®) in aneurysm models of varying vessel curvature as well as in a patient-specific model using Computational Fluid Dynamics. We investigated how these stents modify hemodynamic parameters such as aneurysmal inflow rate, stasis, and wall shear stress, and how such changes are related to the specific designs. We found that the flow damping effect of stents and resulting aneurysmal stasis and wall shear stress are strongly influenced by stent porosity, strut design, and mesh hole shape. We also confirmed that the damping effect is significantly reduced at higher vessel curvatures, which indicates limited usefulness of high-porosity stents as a stand-alone treatment. Finally, we showed that the stasis-inducing performance of stents in 3D geometries can be predicted from the hydraulic resistance of their flat mesh screens. From this, we propose a methodology to cost-effectively compare different stent designs before running a full 3D simulation.

Flow dynamics is a key player in the initiation and progression of vascular diseases such as atherosclerosis and cerebral aneurysms [1–4]. Numerous hemodynamic parameters, such as wall shear stress (WSS), pressure, oscillatory shear index, wall shear stress gradient, impingement size on the arterial wall, and residence time of blood, have been postulated to indicate the tendency for initiation or progression of these vascular pathologies and to evaluate the effectiveness of medical devices in the treatments of such diseases [1–4]. However, in vivo measurements of these hemodynamic parameters for patients are difficult and often cost prohibitive. The combination of noninvasive diagnostic tools (e.g. MRI, CT, or ultrasound) and image-based computational fluid dynamics (CFD) techniques provides an alternative to in vivo measurements to estimate these patient-specific hemodynamic parameters [5–12]. Such image-based CFD analysis has the potential to provide key hemodynamic feedback for prospective studies of vascular diseases and to plan for individual therapeutic options [6,11,13]. Although the application of image-based CFD is rapidly advancing, the ever-present uncertainties in CFD analysis need to be evaluated. In particular, CFD outputs such as WSS or WSS gradients are extremely sensitive to the acquired in vivo geometry. The accuracy and reproducibility of the image-based CFD geometries depend on the orientation of the subject, physiological condition of the subject, variation in vascular structure, contrast-media injection techniques, and operator-dependent decisions in converting the medical images to CFD models [14,15]. Such variations produce poor geometric renditions that can generate as much as 60% variation in hemodynamic parameters obtained using CFD, especially in complex flow regions such as bifurcation apexes, anastomoses, flow separation zones, and aneurysm inflow zones [8,15–17]. Smoothing can reduce poor geometric renditions [16], but the process is somewhat subjective, resulting in an unknown deviation from the true in vivo geometry and subsequent in vitro and CFD models. In addition, the validity of CFD results relies heavily on both temporal and spatial boundary conditions [17–19], which are not routinely available in clinical practice. Significant efforts have been made to improve image-based CFD techniques [8,14,16,20–22], but there have been insufficient efforts to validate the CFD results with experiments. In vitro experimental studies have often been employed to investigate the hemodynamics of vascular diseases and mechanical treatment devices, as well as assisting the development of CFD techniques. Rhee et al. and Imbesi et al. explored the influence of aneurysm geometry and intervention through flow visualization techniques [23,24]. Particle image velocimetry (PIV) and particle tracking velocimetry have been utilized to study the influence of intervention on aneurysmal flow [25–29]. Direct in vivo measurements of blood flow through x-ray imaging, MRI, and ultrasound techniques have also been explored [10,30–33]. MRI and ultrasound allow noninvasive measurement of instantaneous velocities in the 3D domain. Based on the field data, velocity gradients and strain rates are obtained to determine shear stresses and shear stress gradients. However, to date, in vitro studies have been limited to 2D flow fields and scaled-up models that provide optical access. These studies experience significant difficulties in reproducing the in vivo geometries [23] and in vivo biological environments. Direct in vivo measurements pose technical shortcomings, such as inadequate resolutions to derive the flow velocity near the wall, uncertainties in wall positions and insufficient velocity vectors to estimate the derivatives in complex flow regions [10,11,30,31,34–36]. One of the clinical applications of CFD is cerebral vascular diseases such as cerebral aneurysms. Subarachnoid hemorrhage following cerebral aneurysm rupture is often catastrophic, resulting in 12.4% of patient death before patients receive medical attention [37]. Recent studies using aneurysm geometry to predict the risks of aneurysm rupture relied heavily on the imaged aneurysm geometry [38–41]. Prospective patient-specific aneurysm studies that combine medical imaging, CFD analysis, and knowledge of biological responses to hemodynamics forces can provide insight into the hemodynamics of cerebral aneurysms, scientific assessments on therapeutic planning and, ultimately, positive clinical outcomes. However, quantitative validation of image-based CFD analysis against experimental and in vivo data has, to date, not been fully addressed. Following a prior CFD study, which focused on the characteristics of the hemodynamics in an aneurysm located on a curved vessel [42], a PIV validation effort was undertaken in our lab, leading to the investigation of flow sensitivity to aneurysm geometric variations. The goals of this study were to validate our CFD results with PIV experiments using an experimental aneurysm phantom and to quantify the influence of geometric variations on the aneurysmal flow dynamics.

Stenting may provide a new, less invasive therapeutic option for cerebral aneurysms. However, a conventional porous stent may be insufficient in modifying the blood flow for clinical aneurysms. We designed an asymmetric stent consisting of a low porosity patch welded onto a porous stent for an anterior cerebral artery aneurysm of a specific patient geometry to block the strong inflow jet. To evaluate the effect of the patch on aneurysmal flow dynamics, we "virtually" implanted it into the patient's aneurysm geometry and performed Computational Fluid Dynamics (CFD) analysis. The patch was computationally deformed to fit into the vessel lumen segmented from the patient CT reconstructions. After the flow calculations, a patch with the same design was fabricated using laser cutting techniques and welded onto a commercial porous stent, creating a patient-specific asymmetric stent. This stent was implanted into a phantom, which was imaged with X-ray angiography. The hemodynamics of untreated and stented aneurysms were compared both computationally and experimentally. It was found from CFD of the patient aneurysm that the asymmetric stent effectively blocked the strong inflow jet into the aneurysm and eliminated the flow impingement on the aneurysm wall at the dome. The impact zone with elevated wall shear stress was eliminated, the aneurysmal flow activity was substantially reduced, and the flow was considerably reduced. Experimental observations corresponded well qualitatively with the CFD results. The demonstrated asymmetric stent could lead to a new minimally invasive image guided intervention to reduce aneurysm growth and rupture.

The size and dome-to-neck ratio of saccular aneurysms are known to influence the risk of their rupture. To better understand the hemodynamics associated with these variables, we constructed 3-D models of sidewall intracranial aneurysms using CFD. The effect of above-mentioned geometric parameters on wall shear stress (WSS) was investigated. Our results show that the dome area affected by higher values of WSS increases with decreasing dome-to-neck ratio. The results also show that the location of maximal WSS is on the artery near the distal end of the neck. The ability to analyze aneurysm hemodynamics in such a manner may eventually help in assessing the rupture risk of real human aneurysms.

In this Brief Communication, the nonlinear stress–strain model for three‐dimensional turbulent flows, as given by Taulbee [Phys. Fluids A 4, 11 (1992)], is expanded upon. That relation represents a closed form solution to the algebraic Reynolds stress model equation set which is obtained from the modeled transport equation for the Reynolds stress. The parameter values, which appear in the linear pressure–strain closure, that were suggested by Taulbee to obtain a simplified stress relation for three dimensions, are justified in this Brief Communication. A stress solution is also presented for a wider range of pressure–strain model parameter values.

In the chapter, a nonlinear stress-strain model, derived from the modeled Reynolds stress transport equation, is modified to account for the near wall effects in wall-bounded turbulent flows. Since it is known that wall reflection of the turbulent pressure field modifies the pressure-strain correlation, the approach taken is to introduce a correction to the coefficients in the closure for the pressure-strain correlation. The stress-strain relation is implemented in the context of the k – ∈ model with a variable Cμ. Results are presented for plane channel flow, and both zero and adverse pressure gradient boundary layers. Favorable results for the anisotropies in the Reynolds stresses are obtained by the new model as validated by comparisons against direct numerical simulation (DNS) and experimental data.

Two physical phenomena have been the primary subject of investigation: (1) multiphase transport in turbulence, (2) realistic chemistry in large scale numerical simulation of turbulent combustion. In addition, two other phenomena have also been considered: (3) scalar mising in turbulence, and (4) magnetohydrodynamic turbulence. This Final Report provides a summary of our accomplishments in research on each of the above four problems.

The research described in this paper is a numerical investigation of the effects of unsteady flow on gas turbine heat transfer, particularly on a rotor blade surface. The unsteady flow in a rotor blade passage and the unsteady heat transfer on the blade surface as a result of wake/blade interaction are modeled by the inviscid flow/boundary layer approach. The Euler equations which govern the inviscid flow are solved using a time accurate marching scheme. The unsteady flow in the blade passage is induced by periodically moving a wake model across the passage inlet. Unsteady flow solutions in the passage provide pressure gradients and boundary conditions for the boundary-layer equations which govern the viscous flow adjacent to the blade surface. Numerical solutions of the unsteady turbulent boundary layer yield surface heat flux values which can then be compared to experimental data. Comparisons with experimental data show that unsteady heat flux on the blade suction surface is well predicted, but the predictions of unsteady heat flux on the blade pressure surface do not agree.

The problem of particle loss to the wall of a narrow rectangular channel through which an aerosol is passing is studied with simultaneous consideration of diffusion and sedimentation. Both slug flow and Poiseuille flow are considered. It is found that the relative importance of diffusion and sedimentation on the fractional penetration depends upon a parameter σ = hvg/D, where h is the half height of the channel, vg is the settling velocity of a particle and D is the Brownian diffusion coefficient. For σ 200, the loss is due to settling. The loss due to the combined mechanism in the range 0·1

Numerical solutions are found for the similarity formulation of the equations, closed with an eddy viscosity model, governing the flow in a buoyant plume in a stratified environment. The effects of the stratification on the velocity and temperature profiles are studied. Comparisons between computed results and experimental data are made.

Aerosol particle deposition due to gravitational settling in a horizontal circular duct is examined for steady laminar flow, which develops from a uniform velocity profile at the entrance to a parabolic velocity profile downstream. Numerical calculation methods, based on the analysis of the limiting trajectories of the particles, are used to determine the deposition efficiency as a function of the duct entrance length. The results show that the deposition for the limiting cases of very large or small settling approach the solutions for deposition in a slug or a Poiseuille flow, respectively. In addition, particle inertial effects were included and for relatively large inertia, the deposition rate was significantly affected.

The quasi-steady creeping flow in a spherical model alveolus has been studied by solving the Stokes equations numerically in order to understand the airflow in the alveolar region of the human lung. The alveolar shape is allowed to change during the respiratory cycle such that the alevolar mouth opening as a fraction of the surface is a function of the lung volume. The complete velocity field in the alveolus is determined from which a hypothetical interface between the tidal and residential airs before and after a respiratory cycle is calculated. The result shows that there is significant mechanical mixing between the two airs and the calculated percentages of mixing in the lung agree favorably with the existing data from single breath measurement using half-micron aerosols.

The problem of particle loss to the wall of an infinitely long horizontal cylinder filled with an aerosol of uniform concentration initially is studied. The particle movements due to the mechanisms of Brownian diffusion and gravitational settling are considered simultaneously. A series solution for the particle distribution is obtained, from which the deposition loss to the wall is calculated. However, for small time, this series solution does not converge rapidly enough for practical computation, thus, an asymptotic expression is developed for this case. The relative importance of diffusion and sedimentation on the deposition efficiency depends upon the parameter σ = v g a /2 D , where v g is the settling velocity, D the Brownian diffusion coefficient and a the radius of the cylinder. For σ

The deposition of aerosol particles from simultaneous diffusion and sedimentation in Poiseuille flow in a horizontal circular tube is studied. The relative importance of settling as compared to diffusion is determined by a parameter σ = v g R/D where v g is the settling velocity. R is the tube radius and D is the Brownian diffusion coefficient. A series solution is found for the concentration distribution near the tube entrance and the results of a numerical solution are presented for the concentration distribution over the penetration distance for various values of σ.

Predictions using turbulence models are reported for the time-averaged heat-flux distributions on the vane and blade surfaces of the Garrett TFE 731-2 HP and Teledyne CAE 702 HP turbines. To provide the proper initial conditions for the boundary layer solution, the stagnation point process starting from the far free stream is considered. The mean velocity and temperature and the turbulence variation along the stagnation streamline are predicted with a Reynolds stress model so as to resolve accurately the turbulent normal stresses that govern the production of turbulence in the stagnating flow. Using the results from the stagnation solution as initial conditions, the k–ε model equations in boundary layer form are solved at midspan for the pressure and suction sides of the vane and the blade, using a pressure distribution obtained from inviscid codes. The predicted surface heat transfer distributions are compared with measurements from short-duration full-stage rotating turbine measurements.

The gravitational settling of monodisperse particles from fully developed laminar flow in a horizontal curved tube is considered. The particle size is small compared with the tube radius, and their concentration is small so that they do not interact with each other or affect the flow. It was found that for sufficiently heavy particles, or for tubes with very small curvature, or for very small flow Reynolds numbers, the settling to the tube surface versus axial distance is much the same as that for a straight tube. However, for the opposite size of these parameters, the settling behavior becomes much different than that of a straight tube. Particles are maintained in the flow in helical spiral motions and do not settle to the tube surface.

The stability of a streaming layer of incompressible, inviscid, self-gravitational fluid bounded in an infinite similar medium is investigated. The critical wave numbers are found when the layer has a linear streaming velocity profile.

The interception deposition on a round-nose wedge is investigated by the use of E. coli bacterial particles. These particles have a self-amplifying property when deposited on surfaces coated with nutrient material. Experimental data show good agreement with theoretical calculations based on boundary-layer theory. The technique is useful whenever the deposition efficiency or the available time for collecting particles on a surface is minimal, especially when the deposition surface is topographically complex.

Comparisons are made between calculated and measured heat-transfer distributions on the midspan locations of the stators and rotors of two turbine stages. The agreement is generally good, except in regions near the leading edge, and is better for blading of higher aspect ratio. It is suggested that the discrepancies near the leading edge are caused by free-stream turbulence, and attempts to improve the modeling of this factor show improved agreement.

Aerosol particle deposition due to simultaneous settling and diffusion from slug or Poiseuille flow in a horizontal parallel plate channel is studied. Solutions are presented for the deposition flux and bulk mean concentration variations along the channel for the case when the settling is large compared to the diffusion.

Impact and wave propagation problems are considered for nonlinearly viscous and nonlinearly elastic materials. The governing partial differential equations are reduced to ordinary differential equations by means of similarity transformations. The resulting non-linear two point boundary value problems are then, in general, integrated numerically, although some closed form solutions are presented.

11 Kaufman, L. G., II et al., "Review of Hypersonic Flow Separation and Control Characteristics," ASD-TDR-62-168, March 1962, Grumman Aircraft Engineering Corp., New York. 12 Werle, M. J., "A Critical Review of Analytical Methods for Estimating Control Forces Produced by Secondary Injection/' NOLTR 68-5, Jan. 1968, United States Naval Ordnance Lab., White Oak, Md. 13 Hawk, N. E. and Amick, J. L., "Two-Dimensional Secondary Jet Interaction with a Supersonic Stream," AIAA Journal, Vol. 5, No. 4, April 1967, pp. 555-660. 14 Zakkay, V., Erdos, J., and Calarese, W., "An Investigation of the Interaction Between a Transverse Sonic Jet and a Hypersonic Stream," NYU AA-68-27, Aug. 1968, Aerospace Labs., New York University, N.Y.

This paper discusses turbulence in the far-field flow approaching a stagnation point tending to decay by dissipation and growing by production due to mean field gradients. Near the surface where the mean flow gradients are steepest, diffusional transport also becomes important. The resulting boundary layer on the surface near the stagnation point may be considered to be pseudoturbulent or disturbed laminar, and the surface friction and heat transfer can be significantly different than the stagnation flow with no turbulence.

Finally, we should mention a problem that can arise with the heat-flux probe when determining Qconvective by means of Eq. (2). It is difficult to know whether Qcooiant actually remains constant, or whether during a test the coolant absorbs heat before it reaches the platinum-film sensor. This is minimized by keeping the exposed glass tube as short as possible on the inlet side and by carefully designing the supporting tube bundles. However, operating experience indicates that Qcooiant does vary and that this probably contributes to the errors noted in Fig. 4.

Predictions using boundary-layer theory with a low-Reynolds number kinetic-energy/dissipation turbulence model are reported for the unsteady heat-flux distributions on the rotor blade surfaces. With an assumed sinusoidal variation for the unsteady surface pressure depicting the effects of convected wake segments, unsteady inviscid-freestream velocity and total enthalpy distributions are determined. Unsteady variations in freestream turbulence due to the wake passings are also considered. The unsteady boundary-layer equations, subject to these freestream conditions, are solved numerically. It was found that most of the unsteady variations in surface heat transfer are due to unsteady pressure changes and not variations in the freestream turbulence. Calculations are made for the Garrett TFE 731-2 HP turbine and the magnitudes of the heat-transfer variations are compared with the measurements of Dunn and Seymour.