Tie Wei

New Mexico Tech, Mechanical Engineering, Faculty Member

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Papers by Tie Wei

Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows

Journal of Fluid Mechanics, 2005

The properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows a... more The properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows are explored both experimentally and theoretically. Available highquality data reveal a dynamically relevant four-layer description that is a departure from the mean profile four-layer description traditionally and nearly universally ascribed to turbulent wall flows. Each of the four layers is characterized by a predominance of two of the three terms in the governing equations, and thus the mean dynamics of these four layers are unambiguously defined. The inner normalized physical extent of three of the layers exhibits significant Reynolds-number dependence. The scaling properties of these layer thicknesses are determined. Particular significance is attached to the viscous/Reynolds-stress-gradient balance layer since its thickness defines a required length scale. Multiscale analysis (necessarily incomplete) substantiates the four-layer structure in developed turbulent channel flow. In particular, the analysis verifies the existence of at least one intermediate layer, with its own characteristic scaling, between the traditional inner and outer layers. Other information is obtained, such as (i) the widths (in order of magnitude) of the four layers, (ii) a flattening of the Reynolds stress profile near its maximum, and (iii) the asymptotic increase rate of the peak value of the Reynolds stress as the Reynolds number approaches infinity. Finally, on the basis of the experimental observation that the velocity increments over two of the four layers are unbounded with increasing Reynolds number and have the same order of magnitude, there is additional theoretical evidence (outside traditional arguments) for the asymptotically logarithmic character of the mean velocity profile in two of the layers; and (in order of magnitude) the mean velocity increments across each of the four layers are determined. All of these results follow from a systematic train of reasoning, using the averaged momentum balance equation together with other minimal assumptions, such as that the mean velocity increases monotonically from the wall.

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Predicting Law-of-the-Wall with LES: Role of SFS and Surface Stress Models

Bulletin of the American Physical Society, Nov 23, 2009

Predicting Law-of-the-Wall with LES: Role of SFS and Surface Stress Models 1 JAMES BRASSEUR, TIE ... more Predicting Law-of-the-Wall with LES: Role of SFS and Surface Stress Models 1 JAMES BRASSEUR, TIE WEI, SANJIV RAMACHANDRAN, Penn State Univ. -In previous work we presented a framework in which largeeddy simulation (LES) can be designed to capture the law-of-the-wall (LOTW) in mean velocity gradient when the first grid level is in the inertial layer. A proper combination of grid aspect ratio (A R ), subfilter-scale (SFS) stress model constant (C t ), and vertical grid resolution is required to suppress a spurious frictional length scale that underlies deviations from LOTW scaling. This occurs when the LES exceeds critical values of: (1) ratio of mean resolved to SFS shear stress (R) at the first grid level, (2) an "LES Reynolds number" (Re LES ), and (3) vertical resolutionthe "High Accuracy Zone" (HAZ) on a plot of R vs. Re LES . Here we demonstrate this framework for 2 eddy viscosity and one non eddy viscosity SFS models, and we show that for the eddy viscosity models both R and Re LES are inversely proportional to , where a and b are model-dependent constants. Commonly applied surface shear stress models create a spurious sink in velocity variance and oscillations in mean velocity gradient at the surface. Correcting the spurious sink both reduces these oscillations and increases the predicted value of the Von Kármán constant (VKC). We also show that C t and A R must be chosen within certain bounds and that the VKC predicted by LES asymptotes to a value of about 0.37 within these bounds when the LES is within the HAZ.

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Scaling properties of the mean wall-normal velocity in the zero pressure gradient boundary layer

Bulletin of the American Physical Society, Nov 21, 2016

Scaling properties of the mean wall-normal velocity in the zero pressure gradient boundary layer ... more Scaling properties of the mean wall-normal velocity in the zero pressure gradient boundary layer TIE WEI, New Mexico Institute of Mining and Technology, JOSEPH KLEWICKI, University of Melbourne -The scaling properties of the mean wall-normal velocity, V (x, y), in zero-pressure-gradient laminar and turbulent boundary layer flows is investigated using numerical simulation data, physical experiment data, and integral analyses of governing equations. The maximum mean wall-normal velocity, V ∞ , and the boundary layer thickness, δ, are evidenced to be the proper scaling for V over most if not the entire boundary layer. This is different from the behavior of the mean streamwise velocity (U ) or the turbulent shear stress (T = -ρ⟨uv⟩), which depend on different characteristic length scales in the regions near to and away from the surface. Insights pertaining to this are further surmised from an analytical relationship for the ratio of the displacement to momentum thickness, i.e., shape factor, H. Integral analyses using the continuity and mean momentum equation show that (U ∞ V ∞ )/u 2 τ = H, where u τ is the friction velocity. Both the laminar similarity solution and DNS data in post-transitional flows convincingly support this relation. Over the transitional regime, sufficiently high quality data is still lacking to check if this relation remains valid.

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A comparison of explosively driven shock wave radius versus time scaling approaches

Shock Waves

Explosively driven shock wave radius versus time profiles are frequently used to document energy ... more Explosively driven shock wave radius versus time profiles are frequently used to document energy release and relative explosive performance. Recently, two universal shock wave radius versus time profiles have been presented in the literature, which demonstrate the ability to represent explosively driven shock wave profiles for all explosive sources in any fluid environment. These two universal shock wave profiles are examined here relative to each other and relative to a commonly used nonlinear shock wave profile, which is fit to experimental data for individual explosive materials. The nonlinear profile, originally developed by Dewey, is examined here, and a universal non-dimensional form of the equation is proposed. The universal shock wave profiles are all found to be relatively similar, but with slight variations in a transition region of non-dimensional radii $$0.15\lesssim R^*\lesssim 2$$ 0.15 ≲ R ∗ ≲ 2 . The variations in this region result in different estimations of energy ...

format_quoteWei-Hargather scaling shows a strong agreement with theoretical shock propagation models, validating its applicability across various scenarios.format_quote

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Rayleigh–Taylor instability with gravity reversal

Physica D: Nonlinear Phenomena, 2021

We present results from Direct Numerical Simulations (DNS) of Rayleigh-Taylor instability at Atwo... more We present results from Direct Numerical Simulations (DNS) of Rayleigh-Taylor instability at Atwood numbers up to 0.9. After the layer width had developed substantially, additional branched simulations have been run under reversed and zero gravity conditions. We focus on the modifications of the mixing layer structure and turbulence in response to the acceleration change. After the gravity reversal, the flow undergoes a complex transient process in which the vertical mass flux changes sign multiple times and, consequently, the buoyancy term in the turbulent kinetic energy transport equation changes its role back and forth from production to destruction. This behavior is examined in detail using the turbulent kinetic energy and mass flux transport equations and time instances when the vertical mass at the centerline crosses zero and reaches local minima and maxima. While the transient process significantly affects the flow anisotropy at all scales, other turbulence characteristics, like the alignment between the vorticity and eigenvectors of the strain rate tensor, retain their fully developed turbulence behavior in the interior of the layer. In addition, after the gravity reversal, the edges of the layer also exhibit characteristics closer to those of the turbulent interior, even as the fluids become more mixed. None of these changes affects the mean density profile, which still collapses among various cases. Such significant changes in some turbulence quantities and not others are difficult to capture with existing turbulence models.

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Integral properties of turbulent natural convection over a vertical flat plate

International Communications in Heat and Mass Transfer

Abstract This paper investigates global integrals of the volumetric, momentum and temperature flu... more Abstract This paper investigates global integrals of the volumetric, momentum and temperature fluxes for turbulent natural convection over a vertical plate (TNCVP). The global integral of the mean continuity equation gives a relation for the mean wall-normal velocity outside the boundary layer as W∞ = − d(∫0∞Udz)/dx where U is the mean velocity in the streamwise x direction and z is the wall-normal direction. The global integral of the mean momentum equation gives a relation for the specific wall momentum flux as uτ2 = gβ∫0∞(Θ∞ − Θ)dz − d(∫0∞U2dz)/dx where uτ is the friction velocity, g is the gravitational acceleration and β is the thermal expansion coefficient. Θ = Tw − T is the difference between the wall temperature Tw and the fluid temperature, and Θ∞ = Tw − T∞ is the difference between the wall temperature and the ambient fluid temperature. Finally, the global integral of the mean heat equation gives a relation for the wall temperature flux as uτθτ = − W∞Θ∞ − d(∫0∞UΘdz)/dx where θτ is the frictional temperature. Based on the global integrals of the momentum and heat fluxes, we propose an indirect determination of uτ and θτ. Given the extreme challenge in direct measurement of uτ and θτ in wall-bounded turbulent flows, the indirect determination proposed here offers a powerful tool to subsequent experimental studies of TNCVP.

Properties of the mean pressure in Rayleigh-Bénard convection

Physics of Fluids

The mean pressure distribution plays an important role in the dynamics of Rayleigh-Benard convect... more The mean pressure distribution plays an important role in the dynamics of Rayleigh-Benard convection (RBC). In this work, the mean momentum balance equation is analyzed to reveal the properties of the mean modified pressure. The main findings of the present work include the following. (i) In a turbulent RBC, the mean modified pressure peaks in the near-wall region, and the peak location is found to scale with the Townsend inner length scale. (ii) In the outer layer of a turbulent RBC, the shape of the mean modified pressure is similar to that of the Reynolds normal stress in the vertical direction. (iii) In a turbulent RBC, the modified pressure has a negative trough in the core of the RBC cell. The negative modified pressure at the RBC mid-height dictates an inequality among key parameters for a turbulent RBC including the Prandtl number, Rayleigh number, rms Peclet number, and thermal displacement thickness. The inequality is confirmed by experimental and direct numerical simulation data.

Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from monodisperse prolate and oblate spheroidal particles

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

A quasi-steady-state model of the dissolution of a single prolate or oblate spheroidal particle h... more A quasi-steady-state model of the dissolution of a single prolate or oblate spheroidal particle has been developed based on the exact solution of the steady-state diffusion equation for mass transfer in an unconfined media. With appropriate treatment of bulk concentration, the model can predict the detailed dissolution process of a single particle in a container of finite size. The dimensionless governing equations suggest that the dissolution process is determined by three dimensionless control parameters, initial solid particle concentration, particle aspect ratio and the product of specific volume of solid particles and saturation concentration of the dissolved substance. Using this model, the dissolution processes of felodipine particles are analysed in a broad range of space of the three control parameters and some characteristics are identified. The effects of material properties indicated by the product of specific volume and saturation concentration are also analysed. The mo...

In-depth characterization and analysis of simple shear flows over regularly arranged micro pillars, I. Effect of fluid inertia

arXiv (Cornell University), Mar 10, 2022

Through high-fidelity numerical simulation, the simple shear flow over regularly arranged micro p... more Through high-fidelity numerical simulation, the simple shear flow over regularly arranged micro pillars has been investigated. The essential issues to be addressed include the characteristics of a simple shear flow over quadrilateral array of micro pillars, the effect of fluid inertia on the basic flow pattern, and the decomposition of the complex surface friction. The results show that the flow is characterized by a series of microscale recirculating eddies in the gaps between the streamwise neighboring pillars. The recirculation of the micro eddies and the oscillation of the overhead flow climbing over the pillar tips create a local flow advection. At smaller Reynolds number, the fluid inertia is weak and the flow patterns are symmetrical about the pillar center. When the Reynolds number is sufficiently large, the fluid inertia takes effect and breaks the symmetrical patterns. The overhead flow tilts downward, forming a spiral long-range advection between the fluid flow above pillar array and the flow in the spaces among micro pillars. The local advection and long-range advection constitute the transport mechanism in wall-normal direction. On micro-structured walls, the total friction includes the reaction forces of micro pillars due to flow shear and flow pressure at pillar surfaces and the reaction force of bottom plane due to flow shear on bottom surface. For larger Reynolds numbers, fluid inertia prevents the fluid from flowing along the curved surface of micro pillars and reduces the equivalent shear stress of the pillar reaction force due to flow shear. At the same time, the fluid inertia makes the overhead flow impact the windward side of micro pillars more strongly and therefore increases the equivalent shear stress of the pillar reaction force due to flow pressure.

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Layered structure of turbulent natural convection over a vertical flat plate

International Journal of Heat and Mass Transfer, 2021

Governing Parameters of Adverse Pressure Gradient Turbulent Boundary Layers

Volume 1: Flow Manipulation and Active Control; Bio-Inspired Fluid Mechanics; Boundary Layer and High-Speed Flows; Fluids Engineering Education; Transport Phenomena in Energy Conversion and Mixing; Turbulent Flows; Vortex Dynamics; DNS/LES and Hybrid RANS/LES Methods; Fluid Structure Interaction; Fl, 2018

We perform a careful nondimensional analysis of the turbulent boundary layer equations in order t... more We perform a careful nondimensional analysis of the turbulent boundary layer equations in order to bring out, without assuming any self-similar behaviour, a consistent set of nondimensional parameters characterizing the outer region of turbulent boundary layers with arbitrary pressure gradients. These nondimensional parameters are a pressure gradient parameter, a Reynolds number (different from commonly used ones) and an inertial parameter. They are obtained without assuming a priori the outer length and velocity scales. They represent the ratio of the magnitudes of two types of forces in the outer region, using the Reynolds shear stress gradient (apparent turbulent force) as the reference force: inertia to apparent turbulent forces for the inertial parameter, pressure to apparent turbulent forces for the pressure gradient parameter and apparent turbulent to viscous forces for the Reynolds number. We determine under what conditions they retain their meaning, depending on the outer v...

Insights into turbulence through high-resolution field simulations

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Scaling patch analysis of turbulent planar plume

Physics of Fluids, 2021

Proper scaling in turbulent planar plumes is investigated here using a scaling patch approach. Ba... more Proper scaling in turbulent planar plumes is investigated here using a scaling patch approach. Based on the scaled boundary conditions, a proper velocity scale for the mean axial flow is the plume centerline velocity U ref = U ctr, and a proper temperature scale for the temperature excess is Θ ref = T ctr − T ∞, where Tctr is the plume centerline temperature and T ∞ is the ambient fluid temperature. By seeking an admissible scaling, a key concept in the scaling patch approach, for the mean continuity, mean momentum, and mean energy equations, respectively, the following is found: (1) a proper scale for the mean transverse flow is V ref = ( d δ / d x ) U ctr, where d δ / d x is the growth rate of the plume width. (2) A proper scale for the Reynolds shear stress is R vu , ref = U ctr V ref = ( d δ / d x ) U ctr 2, a mix of the scales for the mean axial and transverse flows. (3) A proper scale for the turbulent heat flux is R v θ , ref = V ref Θ ctr, a mix of the scales for the mean transverse flow and mean temperature excess. The mean transverse flow thus plays a critical role in the scaling of turbulent planar plumes. Approximate functions are developed for the scaled mean transverse flow, Reynolds shear stress, and turbulent temperature flux, and are found to agree favorably with experimental and numerical simulation data. The integral analysis of the mean momentum equation yields a Richardson number Ri, which remains invariant in the axial direction. The Richardson number is defined as Ri = def g β Θ ctr δ t / ( U ctr V ref ) ≈ 1 / 2, where g is the gravitational acceleration, β is the thermal expansion coefficient, and δt is the plume half-width based on the mean temperature profile. This Richardson number arises directly from the scaling patch analysis of the mean momentum equation, including both the streamwise and transverse velocity scales.

Analyses of buoyancy-driven convection

Advances in Heat Transfer, 2020