Prediction of turbulent wall shear flows directly from wall

The fully elliptic Reynolds-averaged Navier–Stokes equations have been used together with Lam and Bremhorst's low-Reynolds-number model, Chen and Patel's two-layer model and a two-point wall function method incorporated into the standard k-? model to predict channel flows and a backward-facig step flow. These flows enable the evaluation of the performance of different near-wall treatments in flows involving streamwise and normal pressure gradients, flows with separation and flows with non-equilibrium turbulence characteristics. Direct numerical simulation (DNS) of a channel flow with Re =3200 further provides the detailed budgets of each modelling term of the k and ?-transport equations. Comparison of model results with DNS data to evaluate the performance of each modelling term is also made in the present study. It is concluded that the low-Reynolds-number model has wider applicability and performs better than the two-layer model and wall function approaches. Comparison with DNS data further shows that large discrepancies exist between the DNS budgets and the modelled production and destruction terms of the ? equation. However, for simple channel flow the discrepancies are similar in magnitude but opposite in sign, so they are cancelled by each other. This may explain why, even when employing such an inaccurately modelled ?-equation, one can still predict satisfactorily some simple turbulent flows.     

Unsteady interaction of uniformly vortex flows

The problem of the decay of an arbitrary discontinuity (the Riemann problem) for the system of equations describing vortex plane-parallel flows of an ideal incompressible liquid with a free boundary is studied in a long-wave approximation. A class of particular solutions that correspond to flows with piecewise-constant vorticity is considered. Under certain restrictions on the initial data of the problem, it is proved that this class contains self-similar solutions that describe the propagation of strong and weak discontinuities and the simple waves resulting from the nonlinear interaction of the specified vortex flows. An algorithm for determining the type of resulting wave configurations from initial data is proposed. It extends the known approaches of the theory of one-dimensional gas flows to the case of substantially two-dimensional flows. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 55–66, September–October, 1998.     

Boundary layer interaction in three-dimensional flows

An approach known from the theory of matched asymptotic expansions involving the isolation of subregions with different scales is used to study flows which are assumed to be described by the boundary layer equations almost everywhere near the surface except for a fairly narrow zone in which the inflowing boundary layers interact. Two characteristic types of interaction are identified. An approximate theory describing the flow in the interaction zone, which makes it possible to locate the position of the interaction zone on the surface, is proposed. The interaction flow on the end wall of a vane channel is calculated subject to certain simplifications. The results of an experimental investigation of this flow are presented and it is shown that the theoretical model proposed describes the three-dimensional corner separation which occurs in the neighborhood of the line of intersection of the end wall and the convex edge of the vane.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 116–123, May–June, 1988.     

Disturbance growth rate in turbulent wall flows

Disturbance development in turbulent wall flows is numerically investigated. The flows in a circular tube and in a plane channel are considered. The Navier-Stokes equations subjected to the condition of periodicity along the main flow are integrated in time until a statistically stationary “turbulent” flow regime is attained. Then the solution is disturbed and the further evolution of the disturbance is determined by comparing the two solutions, i.e., with and without the disturbance, which are calculated in parallel. It is shown that in the linear stage on average the solutions diverge exponentially. The main result of the study is that the small disturbance growth rate normalized by the wall time scale turns out to be constant, that is, dependent on neither the Reynolds number on the range considered nor the type of the flow: λ⁺ ≈ 0.021. The estimate of the disturbance growth rate is consistent with the previously obtained results concerning downstream disturbance growth and the estimate for the highest Lyapunov exponent calculated for turbulent flow in a plane channel.     

Confined viscoplastic flows with heterogeneous wall slip

The steady, pressure-driven flow of a Herschel-Bulkley fluid in a microchannel is considered, assuming that different power-law slip equations apply at the two walls due to slip heterogeneities, allowing the velocity profile to be asymmetric. Three different flow regimes are observed as the pressure gradient is increased. Below a first critical pressure gradient G ₁, the fluid moves unyielded with a uniform velocity, and thus, the two slip velocities are equal. In an intermediate regime between G ₁ and a second critical pressure gradient G ₂, the fluid yields in a zone near the weak-slip wall and flows with uniform velocity near the stronger-slip wall. Beyond this regime, the fluid yields near both walls and the velocity are uniform only in the central unyielded core. It is demonstrated that the central unyielded region tends towards the midplane only if the power-law exponent is less than unity; otherwise, this region rends towards the weak-slip wall and asymmetry is enhanced. The extension of the different flow regimes depends on the channel gap; in particular, the intermediate asymmetric flow regime dominates when the gap becomes smaller than a characteristic length which incorporates the wall slip coefficients and the fluid properties. The theoretical results compare well with available experimental data on soft glassy suspensions. These results open new routes in manipulating the flow of viscoplastic materials in applications where the flow behavior depends not only on the bulk rheology of the material but also on the wall properties.     

Kinetics of charge-exchange interaction of dense flows

The nonlinear problem of charge exchange between an ion flow and neutral particles is considered. An exact solution of the equations of charge-exchange interaction in plane geometry is found. Parameters determining the effectiveness of interpenetration of dense flows and the structure of the layer of intense interaction are obtained. Institute of Laser Physics, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 11–19, March–April, 2000.     

A calculation procedure for steady two-dimensional elliptic flows

A calculation procedure is presented for predicting steady two-dimensional elliptic flows. The method introduces a density correction concept and an algebraic equation for the velocity correction instead of the troublesome pressure correction equation in the SIMPLER procedure. Computations show that the method has the same rate of convergence as SIMPLER while saving about 20% computational effort per iteration. Although the method is described for steady two-dimensional situations, its extension to three-dimensional problems is very straightforward.     

Reynolds stress and vorticity in turbulent wall flows

Experimental measurements in a boundary layer and a large-eddy simulation of plane channel flow have been used to study the dynamics of vorticity and mass transport in the nearwall region. It was found that Reynolds stress generation occurs in the vicinity of quasi-streamwise vortices, and that smoke particles tend to be ejected from the wall near these vortical structures.     

Static wall layers in plane channel displacement flows

We study steady and pulsating displacement flows of a Bingham fluid by a Newtonian fluid, along a plane channel. For sufficiently large yield stress a static residual wall layer can result during the displacement. The flow is parameterised by the Reynolds number (Re), the Bingham number (B) and the viscosity ratio (M). Perhaps intuitively, thicker layers are found with larger M and at lower Re. The residual layer is formed on the advective timescale of the displacement but drains on a slower timescale governed by M. For larger M truly stationary layers are only found for large t when the layer has thinned sufficiently to become static. Increased Re results in increased energy production locally around the finger. For large enough Re the energy production can play a significant role in yielding the fluid. As the energy production rate increases it also becomes focused around the corner or shoulder region of the front, and spreads axially along the initial part of the residual layer. This causes fluid to yield increasingly far behind the front and allows for the layer to thin. As B increases the static layer tends to decrease (see also [1], [2]). At small Re the static layer thickness appears to be independent of M. At large Re the layer thickness is dependent on M and decreases asymptotically to a constant value as B → ∞.For pulsating displacement flow rates, Q(t) = 2(1 + Asin  ωt) : A ∈ [0, 1) we study two ranges: ωRe ? 2π and ωRe ? 2π. For the viscous regime (ωRe ? 2π) a pseudo-steady 1D model predicts that the residual layer should remain static for 3(1 + Asin  ωt) < MB. In practice we find that partial mobilisation of the residual layer occurs even when this inequality is satisfied, but not if MB becomes significantly larger than 3(1 + A). For ωRe ? 2π we mobilise the layer for significantly larger values of MB and at smaller A, than in the viscous regime. This effect is traced to the occurrence of out-of-phase velocity fluctuations in the displacing fluid within a wall layer close to the interface.     

Evaluation of ejection detection schemes in turbulent wall flows

Velocity techniques for detecting ejections have been systematically examined by separating the detection schemes into trigger and delimiter algorithms. A new technique for grouping ejections based on a period of quiescence between bursts was also developed. The combination of improved ejection detection and the new grouping technique have reduced the error in the time between bursts from 25% to 10%. There is a similar improvement in the uncertainty.A version of this paper was presented at the 1992 Symposium on Turbulence, Rolla, Mo.     

Direct numerical simulation of wall turbulent flows with microbubbles

The marker‐density‐function (MDF) method has been developed to conduct direct numerical simulation (DNS) for bubbly flows. The method is applied to turbulent bubbly channel flows to elucidate the interaction between bubbles and wall turbulence. The simulation is designed to clarify the structure of the turbulent boundary layer containing microbubbles and the mechanism of frictional drag reduction. It is deduced from the numerical tests that the interaction between bubbles and wall turbulence depends on the Weber and Froude numbers. The reduction of the frictional resistance on the wall is attained and its mechanism is explained from the modulation of the three‐dimensional structure of the turbulent flow. Copyright © 2001 John Wiley & Sons, Ltd.     

Approximate calculation of channel flows under force and energy actions

Gasdynamic channel flows under force and energy actions are considered. An approximate method is proposed for solving the gasdynamic equations that describe these flows. Themethod includes the separation of an “active” flow volume in which the integral electric force and applied power, whose densities are assumed to be uniform, are concentrated and the numerical integration of the system of hydrodynamic equations over the entire channel (in laminar and turbulent variants) with the piecewise constant force and energy sources obtained. The results of experimental investigation are presented for the flow that arises after two accessories mounted on the opposite walls of the vertical rectangular channel of constant cross-section, which create a dielectric barrier discharge (DBD actuators). This flow is numerically simulated using the method developed. On the basis of the method proposed the flow characteristics are determined for a model subsonic diffuser on whose lower wall, immediately in front of the separation zone, the DBD actuator is mounted. The efficiency of this accessory in reducing the gasdynamic losses is demonstrated.     

On the Taylor hypothesis in forced unsteady wall flows

Experiments on the modulation characteristics of the wall shear stress τ′-longitudinal velocity u′ and u′−u′ space–time correlations are reported in a forced turbulent channel flow in a wide range of imposed frequencies. The resulting integral and Taylor scale properties are discussed in detail in the low buffer layer under steady and unsteady flow conditions. It is shown that the small-scale turbulence is sensitive to the imposed unsteadiness since the amplitude and phase of the Taylor length scale vary considerably in the imposed frequency range investigated here. The Taylor hypothesis is acceptably valid in steady and unsteady wall layers just above the low buffer layer. Production and instantaneous pressure gradients are mostly responsible for the deviation of the frozen turbulence-state in the viscous and low buffer sublayers.     

A miniature triple hot-wire probe for wall bounded flows

 Four orthogonal and one non-orthogonal miniature triple hot-wire probes have been developed and tested in a two-dimensional turbulent boundary layer. The influence of the different wire configurations on measurements of the Reynolds stresses has been studied. A directional calibration with an analytical solution for the wire response equations was used for the measurements of the non-orthogonal probe and was tested for the orthogonal probes in order to correct their possible geometrical imperfections. It is shown that a directional calibration does not significantly improve the quality of the measurements for precisely manufactured orthogonal probes and that measuring errors are related rather to the measuring volume, the size of the domain of unique solutions for the instantaneous velocity vector and interference effects, i.e. the wire configuration itself. Received: 7 February 1997/Accepted: 18 November 1997     

Shape optimisation of wall structures located in solitary wave flows

ABSTRACT

In this paper, we present a shape optimisation method for wall structures due to the wave force induced by a solitary wave. The fluid is assumed to be incompressible. Introducing the adiabatic assumption in addition, the acoustic velocity method presented by the author's group, the SUPG finite element method, is effectively used. To evaluate the wave force, we use the performance functional, which consists of the sum of the square of the wave force integrated between the starting and final times. The coordinates of the wall structure are regulated to obtain the minimum performance functional. The adjoint equation method is utilised to derive the gradient of the performance functional with respect to the coordinates. The simple weighted gradient method is employed as the minimisation procedure. Two numerical studies show that the results are consistent with existing structures and provide useful information on the practical design of coastal structures.     

Use of concentration-pulsation equation in the calculation of jet-type turbulent flows

An equation for concentration pulsations is derived, and an approximation is given for the unknown correlations in the equation. An approximation is proposed for the probability distribution of the passive-impurity concentration, taking account of intermittency and allowing the effect of pulsations on the jet-flow parameters to be taken into account. Using the semiempirical (e–) model of turbulence and equations for concentration pulsations in the boundary-layer approximation, the characteristics of isothermal submerged axisymmetric jets and of axisymmetric submerged diffusion flames of propane and hydrogen in air are calculated. It is established that with increase in Froude number the intensity of the concentration pulsations decreases both for isothermal jets and for diffusion flames. The concentration pulsations have a significant effect on the characteristics of the turbulent diffusion flame in its initial region. In the absence of buoyancy forces, concentration fluctuations have little effect on the characteristics in the main region of the flame. A burning jet has a longer range than a jet that is not burning. Combustion has little effect on the intensity of velocity and concentration pulsations. The approaches that are widely used at present for the theoretical investigation of the turbulent mixing of jet-type flows use, as closure relations, a two-parameter model of turbulence consisting of semiempirical differential equations [1, 2]. As a rule, one of the equations in the turbulence model is an equation for the turbulent energy, (u is the pulsational component of the velocity; = 1, 2, 3; are the averaging brackets), and the other is either an equation for the integral scale L of the turbulence [3], or an equation for different combinations of these parameters—the turbulent viscosity [4], the the dissipation rate e²/ [5], etc. The need to use such an approach is associated primarily with the possibility of calculating mean parameters and turbulence characteristics of complex non-self-similar flows depending on the previous development of the flow. In addition, by this means of closure it is possible, using a semiempirical equation for the concentration pulsations [6, 7] (c is the mass concentration) to calculate the meansquare value of the concentration pulsations and also to determine the intermittency coefficient and the distribution function of the probability density P(c). A knowledge of these values is particularly important in investigating turbulent mixing in the presence of diffusion combustion. It is known [8] that pulsations of the gasdynamic parameters must be taken into account in describing turbulent combustion, since the calculation of diffusion-combustion characteristics in the quasilaminar formulation does not allow a number of qualitative features of the process to be taken into account. Despite the many works on turbulent-flow calculations now available, there has been little investigation of a whole series of aspects of this type of flow. For example, there has not been sufficient study of the effect of the buoyancy forces arising because of the density difference between jets of different gases on the level of the concentration pulsations. Very little data is available on the effect of combustion on the turbulent flow characteristics. The present work takes up these questions. A semiempirical equation is proposed for the concentration pulsations. This equation, which is related to the (e–) model of turbulence developed in [4], is tested in calculations of isothermal jets and also diffusional combustion flames. Particular attention is paid to the behavior of the concentration pulsations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 46–55, September–October, 1978.It remains to thank A. N. Sekundov for formulating the problem and for his interest in the work, and also V. R. Kuznetsov and I. P. Smirnova for useful discussions.