Showing papers in "Fluid Dynamics in 2021"

Prandtl’s Secondary Flows of the Second Kind. Problems of Description, Prediction, and Simulation

Abstract: The occurrence of turbulent pulsations in straight pipes of noncircular cross-section leads to the situation, when the average velocity field includes not only the longitudinal component but also transverse components that form a secondary flow. This hydrodynamic phenomenon discovered at the twenties of the last century (J. Nikuradse, L. Prandtl) has been the object of active research to the present day. The intensity of the turbulent secondary flows is not high; usually, it is not greater than 2–3% of the characteristic flow velocity. Nevertheless, their contribution to the processes of transverse transfer of momentum and heat is comparable to that of turbulent pulsations. In this paper, a review of experimental, theoretical, and numerical studies of secondary flows in straight pipes and channels is given. Emphasis is placed on the issues of revealing the physical mechanisms of secondary flow formation and developing the models of the apriori assessment of their forms. The specific features of the secondary flow development in open channels and channels with inhomogeneously rough walls are touched upon. The approaches of semiempirical simulation of turbulent flows in the presence of secondary flows are discussed.

Onset of Rayleigh–Taylor Convection in a Porous Medium

Abstract: The Rayleigh–Taylor instability and the initial stage of density-driven convection in a porous medium is simulated numerically in reference to geologic problems. A two-layer fluid system in which the lower layer is formed by pure water and the upper layer by an aqueous solution of salts is considered. The upper layer is more dense and viscous. The determination of the characteristic time of the onset of convection in the numerical solution is discussed. The parameters which depend on and do not depend of the initial density fluctuations are revealed. The effect of the viscosity contrast on the onset and development of convection flow and mass transfer is analyzed. The quantitative discrepancies related to neglecting the viscosity contrast in geologic fluids are estimated.

A Very Large Eddy Simulation Model Using a Reductionist Inlet Turbulence Generator and Wall Modeling for Stable Atmospheric Boundary Layers

Abstract: Despite many advances in numerical simulation of stable boundary layers (SBL), most of the models developed are complex and computationally expensive. A computational fluid dynamics (CFD) strategy is proposed that combines very large eddy simulation (VLES) with a reductionist inflow turbulence generator and wall modeling aimed at affordable and practical simulation of SBL. Unlike the standard LES requiring the filter width to be of the scale of grid size, the filter width in VLES can be set at a value between the grid size and the large characteristic length scales of the flow. This strategy, along with the application of wall treatments, results in the significant reduction of computational costs. Moreover, the reductionist approach of the inflow turbulence generator minimizes the number of required input parameters to the model, which makes the model suitable for practical applications. A series of sensitivity studies are conducted to refine the numerical parameters including the grid resolution, filter width, and the inflow turbulence generator variables controlling the length and time scales of the eddies generated at the inlet. The performance of the model is successfully evaluated against wind-tunnel measurements for mean velocity, mean temperature, and turbulence profiles for four different thermal stability levels ranging from weak to strong stability. The spectral analysis of the model for velocity components, temperature, momentum, and heat fluxes showed that the model is capable of successfully resolving the energy cascade for almost two orders of magnitude of wave numbers and partially matching the well-known log-log slopes for the inertial subrange.

Investigation of Convection in the Upper Mantle Connected Thermomechanically with the Subduction Zone and Its Geodynamic Application to the Arctic Region and North East Asia

Abstract: The analytical solution to the problem of thermal convection in the upper mantle adjoined to the subduction zone is constructed. The results of seismotomographic mantle shooting are used in the formulation of problem. The corresponding nonlinear problem of mathematical physics can be integrated analytically and reduced to a significantly simpler system of nonlinear algebraic equations. The main aim of the present study is to justify mathematically a new regional model of evolution of the Arctic and North East Asia lithosphere [1–5]. In particular, the possibility of existence of the single -cell flow structure strongly stretched in the horizontal direction in the upper mantle is needed to test.

Liquid Draining Through Multiple Ports: An Investigation on Air Core Vortex Formation

Abstract: The phenomenon of air core vortexing in liquid draining through cylindrical tanks can have serious adverse effects on many engineering systems. Hence, suppression of such vortices is necessity in these applications. In the present work, the influence of initial rotation on vortexing phenomenon with different drain port configurations with constant port diameter (d = 10 mm) are investigated using multiple ports. In all the configurations considered, there is a concentric port (circular) in common surrounded by other ports (circular) placed equidistant from the center. In this paper, vortexing phenomenon is studied by varying the number of surrounding ports and their eccentricity. Draining is allowed through one or more surrounding ports simultaneously. Before draining, circulation is provided to the liquid column by means of rotation (40–240 rpm) using a motorized stirrer where rotational speed can be controlled. Results of this study reveal that for all the drain port configurations, as eccentricity increases, the vortex gets suppressed and hence the draining time decreases. The result also shows that the central port is the key contributor to the vortex formation and for lower values of eccentricity, as the number of surrounding ports increases, vortex is progressively suppressed. Literature reveals that all vortexing studies reported so far were either with single or two drain ports. On multiple drain ports (number of drain ports more than 2), no investigations have ever been reported. Hence, the current study is the first of its kind being presented in this paper.

Two-Dimensional Numerical Study of the Pulsed Co-Flow Jet

Abstract: Two-dimensional flow of the pulsed co-flow jet (CFJ) and the influence of the pulsed parameters on the lift and power consumption are investigated numerically. Firstly, the jet channel of traditional CFJ airfoil is improved. The stall margin is increased by 3° compared with the corresponding traditional CFJ airfoil, and the lift is increased, while the drag is reduced significantly. Then, the influence of the pulsed parameters, such as the pulse waveform, including sinusoidal and rectangular waves, the duty cycle, and the pulse frequency on the lift and power consumption are presented and analyzed in detail. It is concluded that, compared with the steady CFJ, the pulsed CFJ possesses much better ability in suppressing separation and can improve the lift characteristics significantly with limited cost of power consumption. For example, at an angle of attack of 20° flow separation occurs severely, when the steady CFJ is adopted; however, the airflow becomes fully attached on the upper airfoil, when the rectangular pulsed CFJ is employed. As a result, the lift corresponding to the rectangular wave is higher than that of the sinusoidal wave. The results also indicate that the lower duty cycle and pulse frequency can lead to the higher lift but with more power consumption.

Dynamics of a Spherical Bubble in Non-Newtonian Liquids

Abstract: A series of the problems of dynamics of a spherical gas cavity with the uniformly distributed pressure inside and, in particular, without pressure are considered within the framework of hydrodynamic theory of incompressible power-law non-Newtonian liquids. A special attention is given to investigation of the behavior of solutions as functions of the exponent (index) in the power-law non-Newtonian model and determination of the extreme properties of the solutions. The problems of calculation of the necessary external pressure that leads to conservation of the kinetic energy of liquid or the dissipation rate in the process of compression are solved. Other solutions are constructed in a particular case of the Newtonian model. They represent the exact implementation of the linear-resonance behavior of the cavity radius within the framework of the nonlinear formulation of problem and, on the contrary, the law of cavity dynamics under a given harmonic external pressure at the linear-resonance frequency is corrected using numerical methods. The law of dependence of the concentration of the kinetic energy of liquid on the index in the non-Newtonian model and the generalized Reynolds number is established analytically and numerically under the piecewise constant external pressure in the case of the vacuum cavity. It is shown that for a certain indices there is no energy concentration at all. The critical values of the generalized Reynolds number at which the energy concentration also disappears are calculated for the remaining indices. The total energy dissipation is minimized in the case of the cavity occupied by a gas.

The Effect of Non-Uniform Compression of an Elastic Plate Floating on the Fluid Surface on the Development of Unsteady Flexural-Gravity Waves

Abstract: The solution to the time-dependent 3D hydroelastic problem of vibrations of a thin elastic plate floating on the surface of a heavy fluid of finite depth under the action of unsteady external pressure is obtained within the framework of the linear formulation. The effect of the longitudinal, transverse, and shear compression of the plate on the development of flexural-gravity waves is studied. As examples, the periodic and pulse impact of a load is considered.

Tangential Shear Stress under the Periodic Flow of a Viscoelastic Fluid in a Cylindrical Tube

Abstract: The problem of investigation of unsteady tangential shear stress under the periodic laminar flow of a viscoelastic fluid in a cylindrical tube is considered on the basis of the Maxwell model. Formulas for the dynamic-response and frequency characteristics are obtained. The effect of the oscillation frequency, the acceleration, and the relaxation properties of fluid on the tangential shear stress is studied by means of numerical experiments. It is shown that the viscoelastic properties of fluid, as well as its acceleration, act as the limiting factors for using the quasi-stationary approach.

Evolution of a Phase Interface in the Displacement of Viscous Fluids from a Porous Medium

Abstract: The process of displacement of a viscous fluid from a porous medium is simulated numerically with regard to the capillary effects. The surface area of the phase interface is calculated at each instant of time. The effect of the constitutive parameters on variation in the surface area of the phase interface is studied. The experiments on displacement of oil by water from Neocomian sandstones are described. The experimental data are compared with the results of the numerical simulation.

Investigation of the Flow Structure in a Model Scramjet Air Intake with Transverse Hydrogen Fuel Injection into Supersonic Crossflow

Abstract: Combustion flow inside the channel of a model scramjet air inlet with transverse hydrogen fuel injection from the bottom wall is investigated. The OH-concentration and pressure distributions that replicate qualitatively the flow structure observed in experiments are obtained. Several different mechanisms of formation of shock waves in the investigated experimental facility are distinguished. In analyzing the structure of fuel jet, satisfactory quantitative agreement with the calculation results of other authors is obtained. It is shown that the shock-wave structure affects significantly combustion enhancement.

Heat Transfer and Ionization in Non-Equilibrium Hypersonic Flow Past a Blunt Plate

Abstract: The processes of heat transfer and air ionization in gas flow in the neighborhood of blunt plates of bluntness radii Rn = 0.2 and 0.66 cm are simulated numerically over a wide free-stream-parameter range. The temperature fields of the translational and vibrational degrees of freedom of molecular components and the number densities of atomic and molecular components as well as the electron number densities in the neighborhood of the surface are constructed. The convective heat flux densities calculated are compared with the data predicted by the Fay–Riddel, Detra–Kemp–Riddel, and Fenster correlation relations. In the cases considered the volume fraction of ionized components is not greater than 1%. However, the regimes of strong and weak ionization are distinguished. In the present study the boundary between the two regimes is determined from the critical electron number density found for the radio-wave frequencies of 3.3–35 GHz used in the RAMC-2 flight experiment to measure the electron number densities.

Vertical Momentum Transfer Induced by Internal Waves in a Two-Dimensional Flow

Abstract: Free internal waves in a two-dimensional vertically inhomogeneous stratified flow are considered in the Boussinesq approximation with account of the Earth’s rotation. The equation for the amplitude of the vertical velocity of a fixed mode of internal waves has complex coefficients; therefore, the eigenfunction and the wave frequency are complex. The imaginary part of frequency is small and can be both positive and negative. For this reason, both weak damping and weak strengthening of the wave are possible depending on the wavenumber and the mode number. The vertical wave momentum fluxes are nonzero and can be greater than the corresponding turbulent fluxes.

Transition Problem and Localized Turbulent Structures in Pipes

Abstract: In the classical experiments of O. Reynolds made in 1883 the critical value of a dimensionless parameter, named now the Reynolds number, $${\text{R}}{{{\text{e}}}_{c}} \approx 2000$$ , was determined. As this value is exceeded in a pipe of circular cross-section, a turbulent flow regime can occur. The attempts to define this value more exactly undertaken during the twentieth century have not met with success. In this study, we present a review of theoretical, experimental, and numerical investigations of flows in a round pipe at the stage of transition to turbulence performed in recent years, which make it possible to formulate a new view on the nature of laminar-turbulent transition in these flows.

Fine Structure of the Spreading Pattern of a Freely Falling Droplet in a Fluid at Rest

Abstract: High-resolving photo and videorecording was used to visualize the fine structure of the flow pattern upon the coalescence of a droplet, $$0.39 < D < 0.43$$ cm in diameter, falling at a velocity $$3.1 < U < 3.9$$ m/s with water in a reservoir. The spreading of droplets of water, water solution of ink, and copper and iron sulphates is studied. For all pairs of substances, in addition to cavities, crowns, and sheets with shaped outer edges, capillary waves radiated by the annular region of fluid coalescence and thin jetlets at the cavity bottom and the crown walls were observable in the splash formation regime. The jetlets penetrate the sheet and emerge from the tooth tips in the form of spikes. Sequences of small droplets fly out from the spike tips, whose positions change with time. The fluid acceleration is favored by the conversion of the available potential energy upon the annihilation of the free surfaces of the coalescing fluids.

Dynamic Modeling of Heated Oscillatory Layer of Non-Newtonian Liquid

Abstract: In this work, we have effectively used the numerical inversion of the Laplace transform to study the time-dependent thin heated film flow of a viscoelastic fluid flowing on an infinitely long flat substrate. Exact and analytical solutions are obtained in some limiting cases. The model describing this problem is a system of equations, coupling the linearized Navier–Stokes equation of the viscoelastic fluid with regard for gravity as an external force and the temperature relation for the energy profile. By assuming that the fluids are incompressible, we first derive a new system of equations, by taking into account additional terms, due to the insoluble surfactants and the viscoelastic properties. The velocity and temperature profiles are shown and the influence of coupling constant, viscoelastic parameters and the interfacial surfactants on the liquid film are discussed in detail. The validity of our solutions is verified by the numerical results to show the effects of different parameters involved and to show how the fluid flow evolves with time.

Motion of a Load over an Ice Sheet with Non-Uniform Compression

Abstract: The linear hydroelastic problem of the motion of a rectangular external pressure zone over an unbounded ice sheet floating on the fluid surface is considered. The ice sheet is simulated by a thin elastic plate with taking into account the longitudinal, transverse, and shear compressive forces. The external load describes the motion of an air-cushion vehicle. The solution to the time-dependent problem of instantaneous start of the load and its successive rectilinear motion at constant velocity is constructed. The steady-state wave motion developed in large times is investigated. The vertical deflections and strains of the ice sheet, as well as the wave forces acting on the vehicle, are determined.

Electrostatic Instability of the Higher-Order Azimuthal Modes of a Charged Jet

Abstract: The higher-order azimuthal modes of a charged jet of ideal incompressible conducting liquid that moves relative to the surrounding dielectric medium are first investigated. It is shown that there are thresholds of the surface electric charge density above which electrostatic instability of the parent jet surface is implemented. The instability manifests itself in ejection of daughter jets, which are thinner by approximately two orders of magnitude and thereafter disintegrate into droplets. As the mode number increases and the jet velocity relative to the medium decreases, the threshold heights increase. A similar phenomenon is recorded in reference to the velocity of the relative motion of jet and medium. In this case the instability is called aerodynamic but it is implemented at fairly high speeds.

Mass Exchange between the Atmosphere of Turbulent Vortex Ring and the Surrounding Medium

Abstract: Mass exchange between the atmosphere of turbulent vortex ring and the surrounding medium is investigated in the initial stage of motion using the shadow visualization method. For this purpose, vortex rings in which the liquid has a different density as compared with the density of the surrounding medium are generated. The experiments are carried out for various values of the density differences, the velocities, and the vortex sizes. The characteristic time and space scales of mass exchange are determined. It is concluded that the basic mechanism of mass exchange is turbulent diffusion. The turbulent diffusion coefficient in the atmosphere of vortex ring is estimated using the characteristic time of mass exchange.

Control of Cross-Flow in a Three-Dimensional Boundary Layer Using a Multidischarge Actuator System

Abstract: Wind tunnel experiments on the control of flow in a three-dimensional boundary layer are performed using a multidischarge actuator system. The boundary layer was produced on a swept plate with an induced streamwise negative pressure gradient. The actuator system used a near-surface barrier discharge for producing a unidirectional three-dimensional force action over a lengthy region of the plate surface. The possibility of considerably reducing the cross-flow velocity and mitigating the intensity of stationary vortices that produce the cross-flow instability by means of the action of an actuator system is confirmed.

Deformation of an Inviscid Magnetizable Liquid Drop in a Non-Stationary Magnetic Field

Abstract: Variation in the shape of a magnetizable liquid drop suspended in another immiscible magnetizable liquid in the presence of a non-stationary uniform magnetic field is theoretically investigated in the case of high Reynolds numbers. The system of equations consists of the continuity equation for incompressible liquid, the equation of motion for an ideal incompressible liquid, and Maxwell’s equations in the quasi-stationary and ferrohydrodynamic approximations. To solve the problem, the representation of the magnetic field strength and the liquid velocity in form of a multipole expansion expressed in terms of irreducible tensors is used. In such an approach the magnetic field strength and the velocity can be sought for in the form of series with vector and tensor coefficients for which some relations are obtained that make it possible to determine the coefficients. Using these relations, the coefficients are sought in the form of asymptotic expansions in a parameter whose smallness ensures small deformations of the drop. The flow velocity, the magnetic field strength, and the shape of drop are found correct to terms of the first order with respect to the small parameter. The problems of forced and natural drop oscillations generated by switching on instantaneously-applied harmonically oscillating and rotating magnetic fields are solved.

Investigation of Slender Bodies at Hypersonic Mach Numbers

Abstract: Tests were carried in a shock tunnel to determine the heating rate and the wall pressure on a test model flying at hypersonic velocity. The experiments were performed at Mach M = 6.5 and a total enthalpy of 1.2 MJ/kg. Helium was used as the driver gas and air as the driven gas. The effective test time during the tunnel testing was 3.5 ms. The vacuum sputtered gages were used to evaluate the heating rate on the test model. The evaluated heating rate agrees well with numerical simulation. The experimentally measured pressure also agrees with computational fluid dynamics

The Use of a Supersonic Jet of Gas Activated in a Microwave Discharge in Diamond Deposition

Abstract: The gas-jet method of the deposition of diamond-like structures using super-high-frequency (SHF) discharge for activating gases is considered. Direct statistical simulation is applied to analyze the gasdynamic processes occurring in the conditions of the gas-jet deposition of diamond structures. An activated gas flow in a nozzle is investigated and a considerable influence of the processes in the compressed layer formed near the substrate on the rate of synthesis of diamond structures is established. The regimes of flow of mixture components activated in the discharge chamber toward the substrate are determined and a considerable deceleration of heavy components in the compressed layer is found to exist. It is shown that with increase in the pressure in the deposition chamber from 10 to 80 Torr the crystal growth rate increases fourfold at the expense of an increase in the specific flux of the activated components toward the substrate.

Non-Newtonian Fluid Film Flowing Down an Inclined Plane with a Periodic Topography

Abstract: Flow of the thin layer of a nonlinearly viscous fluid subject to the gravity force down an inclined plane is considered. The capillary forces are assumed to be significant and rheology is described by the power law. The effect of a small periodic topography applied to the plane on the characteristics of steady-state flow and its stability is studied in the linear approximation; the calculations are carried out for the sinusoidal topography. It is shown that, regardless of rheology, the film on the plane with topography has the greater mean thickness as compared with the flat plane at the same flow rate, variation in the mean thickness being proportional to the second power of the topography amplitude. The variations in the increments of the normal modes and the critical Reynolds number are also proportional to the second power of the topography amplitude. The long-wave topography increases the critical Reynolds number, for dilatant fluids this effect being reached at the smaller periods than for pseudoplastic fluids.

Numerical Simulation of Disturbance Evolution in the Supersonic Boundary Layer over an Expansion Corner

Abstract: The linear and nonlinear stages of disturbance development in the supersonic boundary layer over a 10° expansion corner is investigated numerically within the framework of Navier—Stokes equations for Mach number 3. The effect of sudden flow expansion on the disturbance evolution is analyzed. The flow stabilization effect observable in the aerodynamic experiment is also discussed.