Subgrid continuum modeling of particle motion in a turbulent flow

An Eulerian continuum approach to modeling the motion of dispersed particles within the framework of the large-eddy simulation method is developed. The approach is based on a kinetic equation for the filtered probability density function for the particle velocity in a turbulent flow. Models for the subgrid turbulent stresses of the dispersed phase are presented.     

Investigation of scale efect for the computation of turbulent flow around a circular cylinder

In order to investigate the scale efect of turbulent flow around a circular cylinder, two similarity numbers(criteria) based on turbulent kinetic and dissipation rates associated with the fluctuation characteristics of turbulence wake are deduced by analyzing the Reynolds averaged Navier–Stokes equations(RANS). The RNG k–ε models and finite volume method are used to solve the governing equations and the second-order implicit time and upwind space discretization algorithms are used to discrete the governing equations. A numerical computation of flow parameters around a two-dimensional circular cylinder with Reynolds numbers ranging from 102to 107is accomplished and the result indicates that the fluctuation of turbulence flow along the center line in the wake of circular cylinder can never be changed with increasing Reynolds numbers when Re3 × 106. This conclusion is useful for controlling the scale of numerical calculations and for applying model test data to engineering practice.     

Investigation of scale effect for the computation of turbulent flow around a circular cylinder

In order to investigate the scale effect of turbulent flow around a circular cylinder, two similarity numbers （criteria） based on turbulent kinetic and dissipation rates associ- ated with the fluctuation characteristics of turbulence wake are deduced by analyzing the Reynolds averaged NavierStokes equations （RANS）. The RNG k-s models and finite volume method are used to solve the governing equations and the second-order implicit time and upwind space discretization algorithms are used to discrete the governing equations. A numerical computation of flow parameters around a two-dimensional circular cylinder with Reynolds numbers ranging from 102 to l07 is accomplished and the result indicates that the fluctuation of turbulence flow along the center line in the wake of circular cylinder can never be changed with increasing Reynolds numbers when Re ≥ 3 × 10^6. This conclusion is useful for controlling the scale of numerical calculations and for applying model test data to engineering practice.     

Heat transfer in turbulent flow with radiation for small optical depths

A study of the effects of radiation on the heat transfer in fully developed turbulent flow in a channel is carried out. The analysis is valid for both small optical depths and for the optically thin limit. Nongrey effects are included through use of the total band absorptance.     

Experimental study of turbulent axisymmetric cavity flow

An experimental study is made of turbulent axisymmetric cavity flow. The flow configuration consists of a sudden expansion and contraction pipe joint. In using the LDV system, in an effort to minimize refraction of laser beams at the curved interface, a refraction correction formula for the Reynolds shear stress is devised. Three values of the cavity length (L = 300, 600 and 900 mm) are chosen, and the cavity height (H) is fixed at 55 mm. Both open and closed cavities are considered. Special attention is given to the critical case L = 600 mm, where the cavity length L is nearly equal to the reattachment length of the flow. The Reynolds number, based on the inlet diameter (D = 110 mm) is 73,000. Measurement data are presented for the static wall pressure, mean velocity profiles, vorticity thickness distributions, and turbulence quantities.List of symbols C _f velocity correction factor - C _p static wall pressure coefficient - D diameter of inlet pipe = 110 mm - H step height or difference in radii of two pipes = 55 mm - L cavity length = 300, 600 and 900 mm - n _a , n _w , n _f refraction indices of the medium between the transmitting lens and window, the window itself, and the working fluid - signal validation rate in LDV, Hz - P wall static pressure, Pa - P _ref wall static pressure at x = -70 mm, Pa - r radial distance from centreline, m - r _a radial position of the virtual intersection, m - r _d radial location of the dividing streamline, m - r _f radial position of the real beam intersection, m - Re Reynolds number based on the inlet diameter - R _i inner radius of the cylindrical cavity=110 mm - t thickness of the window, m - T ₁ integral time scale, s - U streamwise mean velocity, m/s - U _c centreline mean velocity, m/s - U _ref maximum upstream velocity at x= -70 mm, m/s - r.m.s. intensity of streamwise, radial and circumferential velocity fluctuations respectively, m/s - Reynolds shear stress, m²/s² - x distance in the streamwise direction, m - x _a streamwise position of virtual intersection, m - x _f streamwise position of real beam intersection, m - x _r mean reattachment length, m - x nondimensional streamwise distance - y distance normal to the wall=R–r, m Greek symbols vorticity thickness - stream function of dividing streamline      

Subgrid modeling of flow processes in an anisotropic fractal medium

Equations are derived for the effective coefficients of random conductivity fields in the stationary problem of flow in an anisotropic medium. For the fields, lognormal statistics is assumed. The problem is solved using the subgrid modeling method. The results of theoretical calculations are compared with the results of direct three-dimensional numerical modeling. The results of numerical and theoretical calculations are shown to be in good agreement with each other.     

A pore scale study on turbulent combustion in porous media

This paper presents pore scale simulation of turbulent combustion of air/methane mixture in porous media to investigate the effects of multidimensionality and turbulence on the flame within the pores of porous media. In order to investigate combustion in the pores of porous medium, a simple but often used porous medium consisting of a staggered arrangement of square cylinders is considered in the present study. Results of turbulent kinetic energy, turbulent viscosity ratio, temperature, flame speed, convective heat transfer and thermal conductivity are presented and compared for laminar and turbulent simulations. It is shown that the turbulent kinetic energy increases from the inlet of burner, because of turbulence created by the solid matrix with a sudden jump or reduction at the flame front due to increase in temperature and velocity. Also, the pore scale simulation revealed that the laminarization of flow occurs after flame front in the combustion zone and turbulence effects are important mainly in the preheat zone. It is shown that turbulence enhances the diffusion processes in the preheat zone, but it is not enough to affect the maximum flame speed, temperature distribution and convective heat transfer in the porous burner. The dimensionless parameters associated with the Borghi–Peters diagram of turbulent combustion have been analyzed for the case of combustion in porous media and it is found that the combustion in the porous burner considered in the present study concerns the range of well stirred reactor very close to the laminar flame region.     

Numerical and experimental study of turbulent impinging twin-jet flow

The two dimensional impinging circular twin-jet flow with no-cross flow is studied numerically and experimentally. The theoretical predications are carried out through numerical procedure based on finite volume method to solve the governing mass, momentum, turbulent kinetic energy and turbulent kinetic energy dissipation rate. The parameters studied were jet Reynolds number (9.5 × 10⁴  Re  22.4 × 10⁴), nozzle to plate spacing (3  h/d  12), nozzle to nozzle centerline spacing (l/d = 3, 5 and 8) and jet angle (0°  θ  20°). It is concluded that the stagnation primary point moves away in the radial main flow direction by increasing the jet angle. This shift becomes stronger by increasing the nozzle to nozzle centerline spacing (l/d). A secondary stagnation point is set up between two jets. The value of pressure at this point decreases by decreasing Reynolds number and/or increasing the jet angle.

The sub atmospheric region occurs on the impingement plate. It increases strongly by increasing Reynolds number and decreases as the jet angle and/or a nozzle to plate spacing increases. The spreading of jet decreases by increasing nozzle to plate spacing. The intensity of re-circulation zone between two jets decreases by increasing of h/d and jet angle. The increase of turbulence kinetic energy occurs within high gradient velocity.     

Calibration ofX-probes for turbulent flow measurements

We compare two methods of calibrating the yaw response of hot-wire probes: (i) the assumption that an effective angle, independent of the flow speed, can be deduced; (ii) the more general approach of determining the yaw response at a number of different speeds. The first, simpler, approach is shown to give surprisingly reasonable results for the usual turbulence statistics, even in high turbulence intensity flows. Some differences in the distribution of the inclination of the instantaneous velocity vector are observed. There is no advantage in using thek ² factor to allow for longitudinal cooling.     

Wall shear-stress extraction by an optical flow algorithm with a sub-grid formulation

In this study,we developed a novel optical-flow algorithm for determining the wall shear-stress on the surface of objects.The algorithm solves the thin-oil-film...     

New experimental methods for turbulent spots and turbulent spirals in the Taylor-Couette flow

 The flow between concentrically counter-rotating circular cylinders is investigated experimentally with respect to the appearance of turbulent spots, combining two new methods, based on digital image processing. The simultaneous visualization of the transition to turbulence in the whole flow field in the gap between the two cylinders leads to a qualitative understanding of the phenomenon of turbulent spots. Quantitative results about spiral turbulence are obtained from measurements based on a time-resolved technique introducing a special method of image processing for long sequences of video frames. Variations of the gap width between the cylinders and the investigation of different boundary conditions at the end plates of the rotating cylinders allow conclusions concerning the importance of locally defined parameters of the flow field. Received: 4 December 1995/Accepted: 15 May 1997     

Nuclear magnetic resonance study of turbulent flow in a pipe

Results are given from an investigation of longitudinal turbulent diffusion by the nuclear magnetic tracer method, and a technique is described for determining the velocity distribution function of the fluid particles in the pipe cross section.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 105–110, November–December, 1971.     

Colour-coding schlieren techniques for the optical study of heat and fluid flow

This survey presents a unified view of the history, rationale, applications, and current status of colour-coding schlieren optical techniques, based on an extensive literature review. The characteristics and advantages of this unique flow visualization tool are discussed in terms of one- and two-dimensional colour-coding, qualitative and quantitative visualisations, and system sensitivity, range and resolution. In particular, the use of matched spatial filters to tailor the schlieren optics for specific applications is stressed. A wide range of past applications in fluid flow and heat transfer is surveyed. Connections are drawn among these applications and some new applications are discussed.     

A numerical study of the turbulent flow around the stern of ship models

The present work is concerned with the numerical calculation of the turbulent flow field around the stern of ship models. The finite volume approximation is employed to solve the Reynolds equations in the physical domain using a body-fitted, locally orthogonal curvilinear co-ordinate system. The Reynolds stresses are modelled according to the standard k-ε turbulence model. Various numerical schemes (i.e. hybrid, skew upwind and central differencing) are examined and grid dependence tests have been performed to compare calculated with experimental results. Moreover, a direct solution of the momentum equations within the near-wall region is tried to avoid the disadvantages of the wall function approach. Comparisons between calculations and measurements are made for two ship models, i.e. the SSPA and HSVA model.     

Experimental study on flow control of the turbulent boundary layer with micro-bubbles

The effect of micro-bubbles on the turbulent boundary layer in the channel flow with Reynolds numbers (Re) ranging from \(0.87\times 10 ^{5}\) to \(1.23\times 10^{5}\) is experimentally studied by using particle image velocimetry (PIV) measurements. The micro-bubbles are produced by water electrolysis. The velocity profiles, Reynolds stress and instantaneous structures of the boundary layer, with and without micro-bubbles, are measured and analyzed. The presence of micro-bubbles changes the streamwise mean velocity of the fluid and increases the wall shear stress. The results show that micro-bubbles have two effects, buoyancy and extrusion, which dominate the flow behavior of the mixed fluid in the turbulent boundary layer. The buoyancy effect leads to upward motion that drives the fluid motion in the same direction and, therefore, enhances the turbulence intense of the boundary layer. While for the extrusion effect, the presence of accumulated micro-bubbles pushes the flow structures in the turbulent boundary layer away from the near-wall region. The interaction between these two effects causes the vorticity structures and turbulence activity to be in the region far away from the wall. The buoyancy effect is dominant when the Re is relatively small, while the extrusion effect plays a more important role when Re rises.     

Consequences of the second law for a turbulent fluid flow

Second Law statements in thermomechanics applicable to turbulent fluid flow, in which the internal energy in a macroscopic field theory includes contributions both from molecular vibrations and from turbulent fluctuations, are discussed. In the absence of turbulence, these statements naturally reduce to the known and accepted Second Law statements for a nonturbulent medium. The usual version of the Second Law statements — which deny the existence of perpetual motion and place restrictions on the constitutive equations —is extended here in the presence of turbulence; and an additional statement is introduced associated with the tendency of turbulent fluctuations to decay in the absence of external work or the addition of thermal heat. The mathematical representations of various Second Law statements are then used to derive several restrictions on the response variables of the macroscopic turbulence theory. Examples of such variables include the rates of production and dissipation of turbulent fluctuations, the rate of thermal entropy production, internal energy (involving constitutive coefficients which may be taken to be the thermal and turbulent specific heats), turbulent viscosity coefficients and other response functions which control the degree of flow anisotropy in the medium. These Second Law restrictions are then applied to a recent theory of macroscopic turbulent flow by the present authors in which fairly general constitutive equations are presented for the dependent variables of the theory. It is found that not only is the range of values of several constitutive coefficients limited by these Second Law restrictions, but the presence of a number of terms in the constitutive equations is entirely denied.