Reynolds Number Effect on the Grid Turbulence Degeneration Law

A comprehensive experimental investigation of the effect of the Reynolds number on the degeneration law for turbulence generated by biplanar and wicker grids is carried out over a wide range of the grid geometry parameters and the flow velocity. It is established that an increase in the flow velocity leads to an increase in the turbulence intensity at a given distance from the biplanar grid and a decrease in the turbulence decay rate downstream of the grid. An empirical relation between the turbulence intensity behind the grid, on the one hand, and the relative distance x/M from the grid and the Reynolds number based on the grid rod diameter and the flow velocity at the grid mesh center, on the other hand, is proposed. For the same relative distance x/M from the grid the intensity of wicker-grid turbulence is higher than in the case of the flow past a biplanar grid.     

Effect of free‐stream turbulence on the boundary‐layer structure with diffusion combustion of ethanol

The effect of turbulization of a subsonic air flow on the boundarylayer structure was experimentally studied during evaporation and combustion of ethanol behind an obstacle 3–6 mm high. It is shown that turbulization increases the thermal boundarylayer thickness by a factor of 2, where as the dynamic boundarylayer thickness changes weakly. For 1–18% turbulence at the entrance, the change in the momentum thickness along the channel is close to the change in the momentum thickness for a laminar isothermal boundary layer without injection. Local regions of elevated turbulence with a high intensity of heat and mass transfer arise in the case of combustion behind the obstacle at a distance of 40–50 obstacle heights.     

Mixing enhancement behind an oblique shock wave

The possibility of mixing enhancement when a design-condition cocurrent jet passes through a stationary oblique shock is investigated. In [4] the effect of such a shock on the mixing layer of flows with Mach numbers M = 3 and 5 was experimentally investigated and it was shown that behind the shock no turbulence is generated. However, irrespective of its effect on the turbulence characteristics, an oblique shock causes deformation of the jet, modifying its dimensions, and in the three-dimensional case the shape of the cross section. The effect of this deformation on mixing, which is shown to be fairly significant, has been investigated theoretically using a numerical method. An approximate relation describing the variation of the maximum admixture concentration in the jet behind the shock is proposed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 61–68, March–April, 1992.The authors are grateful to V. A. Stepanov for useful discussions.     

Probability distribution and conditional averaging in turbulent flows

The results of an experimental investigation of the turbulence characteristics in the plane mixing layer and in the wake behind a cylinder are given. Measurements are made of the distribution of the velocity and temperature probabilities, the intermittency coefficient, and the conditionally averaged values of the square of the velocity and temperature derivatives.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 31–37, November–December, 1977.     

Apparent transition behavior of widely-used turbulence models

The Spalart–Allmaras and the Menter k–ω SST turbulence models are shown to have the undesirable characteristic that, for fully turbulent external flow computations, a transition region can occur whose extent varies with grid density. Extremely fine two-dimensional grids over the front portion of an airfoil are used to demonstrate the effect. As the grid density is increased, the laminar region near the nose becomes larger. In the Spalart–Allmaras model this behavior is due to convergence to a laminar-behavior fixed point that occurs in practice when freestream turbulence is below some threshold. It is the result of a feature purposefully added to the original model in conjunction with a special trip function. This degenerate fixed point can also cause non-uniqueness regarding where transition initiates on a given grid. Consistent fully turbulent results can easily be achieved by either using a freestream turbulence level higher than the threshold or by making a simple change to one of the model constants. Near the area where turbulence initiates, the SST model exhibits sensitivity to numerical resolution, but its solutions are unique on a given grid. Inconsistent apparent transition behavior with grid refinement in this case does not stem from the presence of a degenerate fixed point. A nullcline analysis is used to visualize the local behavior of the model.     

Three-parameter model of shear turbulence

A model of shear turbulence is proposed in which transport equations are used for three flow chracteristics: the energy E, the friction stress — (uv), and the function F, whose dimensionality coincides with that of the quantity E^mLⁿ. Well-known equations are used for the first two quantities, while a special analysis is required to construct the third equation. The constants in the equations are determined by analyzing the flow behind a grid with constant shear and the behavior of the solutions in different flow regions in the channel. The results of a numerical solution for a flow in a channel are given, and the results are compared with the known experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 13–25, May–June, 1978.The authors thank V. M. Ievlev and the participants of the seminars run by G. N. Abramovich and G. A. Lyubimov for discussions of the work.     

Interaction of a normal shock wave with a compressible turbulent flow

A speckle photographic method, which is sensitive to changes of gradients in fluid density, is applied for analyzing a compressible turbulent air flow with density fluctuations. Spatial correlation coefficients, turbulent length scales, and energy spectra are determined under the assumption of homogeneous isotropic turbulence. The experiments are performed in a shock tube where the flow is passed through a turbulence grid. Measurements are taken before and after the turbulent regime interacts with the normal shock wave reflected from the tube's end wall. Amplification of the turbulence intensity by the shock interaction process is verified quantitatively and is shown to be restricted to the lower wave numbers in the spectrum.A version of this paper was presented at the 11th Symposium on Turbulence, University of Missouri-Rolla, Oct. 17–19, 1988.To Professor Dr.-Ing. Klaus Gersten on the occasion of his 60th birthday     

A Robust High-Resolution Split-Type Compact FD Scheme for Spatial Direct Numerical Simulation of Boundary-Layer Transition

In this paper an efficient split-type Finite-Difference (FD) scheme with high modal resolution – most important for the streamwise convection terms that cause wave transport and interaction – is derived for a mixed Fourier-spectral/FD method that is designed for the spatial direct numerical simulation (DNS) of boundary-layer transition and turbulence. Using a relatively simple but thorough and instructive modal analysis we discuss some principal trouble sources of the related FD discretization. The new scheme is based on a 6th-order compact FD discretization in streamwise and wall-normal direction and the classical 4th-order Runge–Kutta time-integration scheme with symmetrical final corrector step. Exemplary results of a fundamental-(K-) type breakdown simulation of a strongly decelerated Falkner–Skan boundary layer (Hartree parameter _H = – 0.18) using 70 mega grid points in space are presented up to the early turbulent regime (Re_,turb 820). The adverse pressure gradient gives rise to local separation zones during the breakdown stage and intensifies final breakdown by strong amplification of (background) disturbances thus enabling rapid transition at moderate Reynolds number. The appearance and dynamics of small-scale vortical structures in early turbulence basically similar to the large-scale structures at transition can be observed corroborating Kachanov's hypothesis on the importance of the K-regime of breakdown for coherent structures in turbulence.     

Free-stream turbulence effects on vortex-induced vibration of two side-by-side elastic cylinders

The effect of free-stream turbulence on vortex-induced vibration of two side-by-side elastic cylinders in a cross-flow was investigated experimentally. A turbulence generation grid was used to generate turbulent incoming flow with turbulence intensity around 10%. Cylinder displacements in the transverse direction at cylinder mid-span were measured in the reduced velocity range 1.45<U_r0<12.08, corresponding to a range of Reynolds number (Re), based on the mean free-stream velocity and the diameter of the cylinder, between Re=5000–41 000. The focus of the study is on the regime of biased gap flow, where two cylinders with pitch ratio (T/D) varying from 1.17 to 1.90 are considered. Results show that the free-stream turbulence effect is to enhance the vortex-induced force, thus to restore the large-amplitude vibration associated with the lock-in resonance. However, the enhancement is significant at a different Strouhal number (St) for different pitch ratios. When the spacing between two cylinders is relatively small (1.17<T/D<1.50), the enhancement is significant at St≈0.1. When the spacing is increased, the Strouhal number at which the enhancement is significant shifts to St≈0.16. This enlarges the range of reduced velocity to be concerned. An energy analysis showed that free-stream turbulence feeds energy to the cylinder at multiple frequencies of vortex shedding. Therefore, the lock-in region is still of main concern when the approach flow is turbulent.     

Experimental investigation of turbulence in a supersonic flow

The structure of disturbances carried by the flow into the working section of a supersonic wind tunnel has been investigated by means of a constant-current hot-wire anemometer. In order to generate the disturbances grids consisting of round rods were introduced upstream from the nozzle throat. It was found that in the working section the disturbances consist of non-correlating vortex, entropy and acoustic modes. The latter is generated by the boundary layer on the nozzle walls and the first two by the grids. The spectral compositions of the various modes are compared. Because of the presence of grid turbulence the point of laminar-turbulent transition in the boundary layer on a flat plate varied widely.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 119–124, May–June, 1990.     

Turbulence intensity and turbulent transport characteristics behind gratings in pipes

The magnitudes of the variance ² of the concentration distribution C(y) of a material being mixed in a stream behind turbulizing gratings in a pipe are measured. The impurity (helium) was inserted in the air stream via a thin pipe mounted directly behind one of the grating orifices. The intensity of the turbulent stream velocity pulsations behind the grating was measured by the method of helium diffusion. Estimates of the magnitudes of the turbulent diffusion coefficient D and the diffusion scale of turbulencel were given on the basis of these measurements. Characteristics of the turbulent stream behind gratings in wind tunnels have been investigated in [1–3], for example. The process of turbulent diffusion behind gratings has been studied to a lesser degree. The flow directly behind the grating is of greatest interest for practice, but in the majority of papers the measurements have been made at a distance x from the grating which exceeds (10–20)M, where M is the distance, or step, between the centers of the grating orifices. Moreover, as a rule, the gratings investigated possessed low hydraulic drag and the intensity of stream turbulence ahead of them was considerably lower than ahead of the technical mixing apparatus.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 36–42, January–February, 1973.     

Calculation of three-dimensional weakly expanding flow in jets and channels

The results are given of a calculation of laminar flow in a channel of square section and the motion of a turbulent jet from a cruciform nozzle in an ambient flow. To calculate the secondary flows, the field of the transverse velocity is decomposed into irrotational and solenoidal components. The results of the calculation of the flow in the channel are compared with the calculations of other authors and experimental data. To calculate the flow in the turbulent jet, a one-parameter turbulence model is used, and the influence of the inhomogeneity of the distribution of the longitudinal component of the velocity on the components of the Reynolds stress tensor is taken into account. The results of calculation of the flow in the jet behind a cruciform nozzle are compared with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 36–44, July–August, 1984.     

Flow and Mixing Fields for Transported Scalar PDF Simulations of a Piloted Jet Diffusion Flame (‘Delft Flame III’)

Numerical simulation results are presented for ‘Delft Flame III’, a piloted jet diffusion flame with strong turbulence–chemistry interaction. While pilot flames emerge from 12 separate holes in the experiments, the simulations are performed on a rectangular grid, under the assumption of axisymmetry. In the first part of the paper, flow and mixing field results are presented with a non-linear first order k–ε model, with the transport equation for ε based on a modeled enstrophy transport equation, for cold and reactive flows. For the latter, the turbulence model is applied in combination with pre-assumed β-PDF modeling for the turbulence–chemistry interaction. The mixture fraction serves as conserved scalar. Two chemistry models are considered: chemical equilibrium and a steady laminar flamelet model. The importance of the turbulence model is highlighted. The influence of the chemistry model is noticeable too. A procedure is described to construct appropriate inlet boundary conditions. Still, the generation of accurate inlet boundary conditions is shown to be far less important, their effect being local, close to the nozzle exit. In the second part of the paper, results are presented with the transported scalar PDF approach as turbulence–chemistry interaction model. A C₁ skeletal scheme serves as chemistry model, while the EMST method is applied as micro-mixing model. For the transported PDF simulations, the model for the pilot flames, as an energy source term in the mean enthalpy transport equation, is important with respect to the accuracy of the flow field predictions. It is explained that the strong influence on the flow and mixing field is through the turbulent shear stress force in the region, close to the nozzle exit.     

Hybrid URANS/LES Turbulence Simulation of Vortex Shedding Behind a Triangular Flameholder

In this study a detached eddy simulation (DES) model, which belongs to the group of hybrid URANS/LES turbulence models, is used for the simulation of vortex shedding behind a triangular obstacle. In the near wall region or in regions where the grid resolution is not sufficiently fine to resolve smaller structures, the two-equation RANS shear-stress transport (SST) model is used. In the other regions with higher grid resolution a LES model, which uses a transport equation for the turbulent subgrid energy, is applied. The DES model is first investigated for two standard test cases, namely decaying homogeneous isotropic turbulence and the backward facing step, respectively. For the decaying homogeneous isotropic turbulence test case the evolution of the energy spectra in wavenumber space for different times are studied for both the DES and a Smagorinsky type LES model. Different grid resolutions are analyzed with a special emphasis on the modeling constant connecting the filter length scale to the grid size. The results are compared to experimental data. The backward facing step test case is used to study the model behavior for a case with a transition region between a RANS modeling approach close to the wall and LES based modeling in the intense shear flow region. The final application is the simulation of the vortex shedding behind a triangular obstacle. First, the influence of the inlet condition formulation is studied in detail as they can have a significant influence especially for LES based models. Detailed comparisons between simulation and experiment for the flow structure past the obstacle and statistical quantities such as the shedding frequency are shown. Finally the additional temporal and spatial information provided by the DES model is used to show the predicted anisotropy of turbulence.     

Evaluation of bubble-induced turbulence using direct numerical simulation

The presented research evaluates the interaction between a single bubble and homogeneous turbulent flow using direct numerical simulation (DNS) approach. The homogeneous single-phase turbulence is numerically generated by passing a uniform flow through grid planes. The turbulence decay rate is compared with experiment-based correlation. The single phase turbulence is then used as an inflow boundary condition for a set of single bubble studies. By estimating the turbulent field around the fully resolved bubble, the effects of bubble deformability, turbulent intensity and relative velocity on the bubble-induced turbulence are investigated. The existence of bubble creates new vortices in the wake region and the enhancement of turbulence is observed in the region behind the bubble. The results show that the magnitude of the turbulence enhancement would increase as the bubble encounters larger liquid turbulent intensity or higher relative velocity. Set of bubble Weber numbers from 0.34 to 3.39 are used to investigate the effect of bubble deformability. The more deformable bubble is the higher the increase in the magnitude of the turbulence enhancement behind the bubble. This research provides systematic insight on the bubble-induced turbulence (BIT) mechanism and is important for multiphase computational fluid dynamics (M-CFD) closure model development.     

Calculation of isotropic turbulence spectrum

The spectral function of isotropic turbulence is obtained on the basis of semi-empirical turbulence theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 161–164, November–December, 1974.     

RANS-based numerical simulation and visualization of the horseshoe vortex system in the leading edge endwall region of a symmetric body

This contribution is aimed at analyzing the capabilities of popular two-equation turbulence models to predict features of 3D flow fields and endwall heat transfer near the blunt edge of a symmetric body mounted on a plate. The configuration studied experimentally by Praisner and Smith is considered. Results obtained with the in-house CFD code SINF and the commercial package ANSYS–CFX are presented and compared. Prediction capabilities of the low-Re Wilcox turbulence model and two versions of the Menter SST model, the original and the modified one, are analyzed in comparison with the experimental data. Special attention is paid to grid sensitivity of the numerical solutions. Advanced visualization of the vortex structures computed is performed with author’s visualization tool HDVIS. It has been established that the Wilcox model is not capable of predicting the development of a multiple-vortex system observed in the experiment upstream of the body leading edge. Both versions of the MSST model produce qualitatively correct results, with a considerable superiority of the modified version when compared with the quantitative data.     

Effect of external turbulence on the development of a turbulent jet

The effect of external turbulent agitation on jet development has been investigated in [1–3]. The difference of the method employed in the present work lies in the assumption that the turbulence scale of the external flow is substantially larger than the turbulence scales in either the jet or the mixing layer. Utilizing this assumption, it becomes possible to solve separately the energy equations for the turbulence of the external flow and of the jet. Solutions obtained on the basis of this assumption are found to be in qualitative agreement with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 24–29, January–February, 1977.     

Turbulence characteristics in plane co-jet flow in an open channel

Results of an experimental investigation of the turbulence characteristics during mixing of a jet with a bounded co-stream are represented in this paper. The investigation is carried out in the m = 0.2–2.0 range of velocity relation coefficients. The influence of the initial difference in the velocities of the streams being intermixed on the level of turbulence intensity in the mixing layer in the main section at up to 100 calibers in length is established. The experiments qualitatively confirmed available results on the dependence of the turbulence intensity on the velocity relation coefficient.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 175–178, March–April, 1977.     

Numerical modeling of a turbulent flow behind a heated grid

A numerical model of the dynamics of turbulence and temperature fluctuations behind a heated grid located in a wind tunnel is constructed on the basis of closed Kármán-Howarth and Corrsin equations. Results calculated by this model are in reasonable agreement with available experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 118–126, May–June, 2009.