Three-dimensional Non-stationary Flow Research Articles

Non-Stationary Helical Flows for Incompressible Couple Stress Fluid

We explored here the case of three-dimensional non-stationary flows of helical type for the incompressible couple stress fluid with given Bernoulli-function in the whole space (the Cauchy problem). In our presentation, the case of non-stationary helical flows with constant coefficient of proportionality α between velocity and the curl field of flow is investigated. In the given analysis for this given type of couple stress fluid flows, an absolutely novel class of exact solutions in theoretical hydrodynamics is illuminated. Conditions for the existence of the exact solution for the aforementioned type of flows were obtained, for which non-stationary helical flow with invariant Bernoulli-function satisfying to the Laplace equation was considered. The spatial and time-dependent parts of the pressure field of the fluid flow should be determined via Bernoulli-function if components of the velocity of the flow are already obtained. Analytical and numerical findings are outlined, including outstanding graphical presentations of various types of constructed solutions, in order to elucidate dynamic snapshots that show the timely development of the topological behavior of said solutions.

THREE-DIMENSIONAL NONSTATIONARY FLOW OF TWO IMMISCIBLE FLUIDS IN A ROTATING HORIZONTAL CYLINDER

The three-dimensional nonstationary axisymmetric flow of two immiscible viscous fluids in a rotating horizontal cylinder is studied. The interface between the fluids is assumed to be flat and undeformable. The full energy condition at the interface is taken into account. The mass forces are neglected. The velocity field of the Himenz type is considered. For the solution of the nonlinear initial boundary value problem, the modified Galerkin method and the Runge-Kutta method have been applied. It is shown that, with an increase of time, the numerical solution of the nonstationary problem tends to the stationary regime.

Influence of the flow structure formation on heat transfer processes in tubes with spiral corrugated inserts

In order to enhance heat transfer processes in elements of power equipment with minimal energy consumption, the concept of partial structure formation of the heat transfer surface was developed. To determine the energy efficiency of partial structure formation of the heat transfer surface with transitional Reynolds numbers, the surface in the form of spiral corrugation is considered. Partial spiral corrugation due to a change in the flow structure makes it possible to increase the convective component of heat transfer with a moderate increase in friction loss in a transient flow regime. Based on direct numerical simulation of the three-dimensional non-stationary flow structure in the initial section of the tube with a spiral corrugated insert with the shock inlet and transition Reynolds number, the relationship between the structure of the disturbed non-isothermal flow and heat transfer rate on the tube surface is shown. The influence of temperature head on the growth rate of perturbations of the boundary layer in the tube, in the boundaries of which low-frequency oscillatory flow processes are formed, leading to an increase in convective heat transfer rate, is shown. The flow nature and changes in hydrodynamic and thermal parameters in the corrugated insert are investigated. The degree of influence of the spiral corrugated insert, not blocking the flow area of the tube, on the development of natural oscillations in the tube is determined. The influence of the pitch of spiral corrugation to the tube axis on the thermal and hydrodynamic processes in it is investigated. The resulting heat transfer enhancement (up to 20 %) with a simultaneous increase in friction loss (up to 7.5 %) correlates with the experimental results of other authors with similar corrugations in the given range of Reynolds numbers.

Dependence of energy characteristics of ascending swirling air flow on velocity of vertical blowing

In the model of a compressible continuous medium, for the complete Navier-Stokes system of equations, an initial boundary problem is proposed that corresponds to the conducted and planned experiments and describes complex three-dimensional flows of a viscous compressible heat-conducting gas in ascending swirling flows that are initiated by a vertical cold blowing. Using parallelization methods, three-dimensional nonstationary flows of a polytropic viscous compressible heat-conducting gas are constructed numerically in different scaled ascending swirling flows under the condition when gravity and Coriolis forces act. With the help of explicit difference schemes and the proposed initial boundary conditions, approximate solutions of the complete system of Navier-Stokes equations are constructed as well as the velocity and energy characteristics of three-dimensional nonstationary gas flows in ascending swirling flows are determined.

Numerical Analysis of the Three-Dimensional Nonstationary Flow of Ideal Gas in the Last Stage of Turbine Machine Taking into Consideration the Nonaxisymmetric Exhaust Pipe Branch

A problem related to the forecast of the aeroelastic behavior and aeroelastic instability of blades (in particular self-oscillations, flutter, and resonance vibrations) becomes of great importance for the development of high-loaded compressor and vent rows and the last turbine stages whose long and flexible blades can be exposed to such phenomena. The solution of this problem requires the development of new models for the nonstationary three-dimensional flow, the use of contemporary numeric methods and the comparison of theoretical and experimental data. This scientific paper gives the data of numerical simulation of the 3-D flow of ideal gas passing through the last stage of turbine machine taking into account the flow nonuniformity caused by guide blades and nonuniform pressure distribution in the exhaust pipe branch and also nonstationary effects caused by blade vibrations. The numerical method is based on the solution of combined aeroelastic problem for the 3-D flow of ideal gas passing through the turbine stage and the nonaxisymmetric exhaust pipe branch including the annular diffuser. To solve the combined problem a partially integral method was used that includes integral equations of gas dynamics (Euler equations) and vibrating blade dynamics (modular approach) at each time step with the information exchange. The given method of the solution of combined aeroelastic problem allows us to predict the amplitude-frequency spectrum of blade vibrations in the three-dimensional flow of ideal gas including forced self-excited vibrations and self-vibrations to increase efficiency and reliability of the blade units of turbine machines.

Numerical modeling of three-dimensional non-stationary flows and heat/mass transfer in a cylindrical liquid bridge in the absence of gravity

Numerical modeling of three-dimensional non-stationary flows and heat/mass transfer in a cylindrical liquid bridge in the absence of gravity

On the dynamics of exotic matter: Towards creation of Perpetuum Mobile of third kind

The one-dimensional dynamics of a classical ideal ‘exotic’ fluid with equation of state p=p(ϵ)<0 violating the weak energy condition is discussed. Under certain assumptions it is shown that the well-known Hwa–Bjorken exact solution of one-dimensional relativistic hydrodynamics is confined within the future/past light cone. It is also demonstrated that the total energy of such a solution is equal to zero and that there are regions within the light cone with negative (−) and positive (+) total energies. For certain equations of state there is a continuous energy transfer from the (−)-regions to the (+)-regions resulting in indefinite growth of energy in the (+)-regions with time, which may be interpreted as action of a specific ‘Perpetuum Mobile’ (Perpetuum Motion). It is speculated that if it is possible to construct a three-dimensional non-stationary flow of an exotic fluid having a finite negative value of energy such a situation would also occur. Such a flow may continuously transfer positive energy to gravitational waves, resulting in a runaway. It is conjectured that theories plagued by such solutions should be discarded as inherently unstable.

A Numerical Method of Moments for Solute Transport in Nonstationary Flow Fields

A Lagrangian perturbation approach has been applied to develop the method of moments for predicting mean and variance of solute flux through a three-dimensional nonstationary flow field. The flow nonstationarity may stem from medium nonstationarity, finite domain boundaries, and/or fluid pumping and injecting. The solute flux is described as a space–time process where time refers to the solute flux breakthrough and space refers to the transverse displacement distribution at the control plane. The analytically derived moment equations for solute transport in a nonstationary flow field are too complicated to solve analytically, a numerical finite difference method is implemented to obtain the solutions. This approach combines the stochastic model with the flexibility of the numerical method to boundary and initial conditions. This method is also compared with the numerical Monte Carlo method. The calculation results indicate the two methods match very well when the variance of log-conductivity is small, but the method of moment is more efficient in computation.

A numerical method of moments for solute transport in physically and chemically nonstationary formations: linear equilibrium sorption with random K d

A Lagrangian perturbation method is applied to develop a method of moments for solute flux through a three-dimensional nonstationary flow field. The flow nonstationarity stems from medium nonstationarity and internal and external boundaries of the study domain. The solute flux is described as a space-time process where time refers to the solute flux breakthrough through a control plane (CP) at some distance downstream of the solute source and space refers to the transverse displacement distribution at the CP. The analytically derived moment equations for solute transport in a nonstationarity flow field are too complicated to solve analytically, a numerical finite difference method is implemented to obtain the solutions. This approach combines the stochastic model with the flexibility of the numerical method to boundary and initial conditions. The developed method is applied to study the effects of heterogeneity and nonstationarity of the hydraulic conductivity and chemical sorption coefficient on solute transport. The study results indicate all these factors will significantly influence the mean and variance of solute flux.

Model of a viscous layer deformation by thermocapillary forces

Three-dimensional nonstationary flow of a viscous incompressible liquid is investigated in a layer, driven by a nonuniform distribution of temperature on its free boundaries. If the temperature given on the layer boundaries is quadratically dependent on horizontal coordinates, external mass forces are absent, and the motion starts from rest then the free boundary problem for the Navier–Stokes equations has an ‘exact’ solution in terms of two independent variables. Here the free boundaries of the layer remain parallel planes and the distance between them must be also determined. In present paper, we formulate conditions for both the unique solvability of the reduced problem globally in time and the collapse of the solution in finite time. We further study qualitative properties of the solution such as its behaviour for large time (in the case of global solvability of the problem), and the asymptotics of the solution near the collapse moment in the opposite case.

Numerical simulation of instabilities and secondary regimes in spherical couette flow

In all previous numerical investigations of spherical Couette flow only axisymmetric regimes were considered. At the same time, in experiments [1–4] it was found that when both spheres rotate and the layer is thin centrifugal instability of the main flow leads to the appearance of nonaxisymmetric secondary flows of the azimuthal traveling wave type. The results of an initial numerical investigation of these flows are presented below. Solving the linear problem of the stability of the main flow and simulating the secondary flows on the basis of the complete nonlinear Navier-Stokes equations has made it possible to supplement and explain many of the results obtained experimentally. The type of bifurcation and the structure of the disturbances whose growth leads to the appearance of three-dimensional nonstationary flows are determined, and the transitions between different secondary regimes in the region of weak supercriticality are described.

Modelling turbulent flows in a plane channel

Two- and three-dimensional non-stationary flows of incompressible viscous fluid in a plane infinite channel are considered. Using efficient computing algorithms based on the Navier-Stokes equations, the flows are modelled in significant time intervals. The classes of two- and three-dimensional non-stationary flows with established integral characteristics are found. Two-dimensional flows only qualitatively reflect the typical singularities of the turbulent flows observed in experiments. Three-dimensional flows are in good agreement (even quantitatively) with turbulent flows. The basic characteristics of turbulent flows (the coefficient of resistance, mean-velocity profile, and the distribution of mean square pulsations of the velocity components) are reproduced with good accuracy in the calculated three-dimensional flows.

Secondary flows in a plane channel: their relationship and comparison with turbulent flows

Two- and three-dimensional non-stationary viscous-fluid flows in a plane channel are considered. By means of efficient computational algorithms for direct integration of the incompressible Navier-Stokes equations the evolution of these flows over large time intervals is simulated. Classes of two- and three-dimensional non-stationary flows with stationary integral characteristics (the flow rate, mean pressure gradient, total energy of pulsations etc.) were found. Such flows are called secondary flows. Two-dimensional secondary flows have only qualitative similarity to turbulent flows observed in experiments. Three-dimensional secondary flows agree very well, even quantitatively, with turbulent flows. The principal characteristics of turbulent flows such as drag coefficient, mean-velocity profile, the distributions of the pulsation velocity components and some others are reproduced in three-dimensional secondary flows with good accuracy.

Calculation of flow around a lifting surface in the case of large deformations

Many studies have been made of the nonstationary flow of an ideal incompressible fluid around a lifting surface. The present state of the numerical methods of solution of this problem is reviewed in [1]. The present paper studies three-dimensional nonstationary flow around a lifting surface which undergoes deformation and behind which a wake vortex surface is formed. The lifting and wake vortex surfaces are represented in parametric form. The metrics of these surfaces are used, and the introduced vortex function is approximated by bicubic splines. For the convenient application of the theory developed here to the flapping flight of insects, for which it is sometimes difficult to distinguish the lateral and trailing edges of the wings, the following terminology is introduced. The part of the edge of the lifting surface from which the wake vortex surface is shed is called the trailing edge. The remaining part is called the leading edge. On the leading edge, the velocity has a singularity. Test calculations have demonstrated the effectiveness of the method.