Numerical study of flows of a viscous compressible gas and of an equilibrium gas mixture in a flat nozzle in the presence of strong blowing

The problem of the interaction of a viscous supersonic stream in a flat nozzle with a transverse gas jet of the same composition blown through a slot in one wall of the nozzle is examined. The complete Navier-Stokes equations are used as the initial equations. The statement of the problem in the case of the absence of blowing coincides with [1]. The conditions at the blowing cut are obtained on the assumption that the flow of the blown jet up to the blowing cut is described by one-dimensional equations of ideal gasdynamics. The proposed model of the interaction is generalized to the case of flow of a multicomponent gas mixture in chemical equilibrium. The exact solutions found in [2] are used as the boundary conditions at the entrance to the section of the nozzle under consideration. The results of numerical calculations of the flows of a homogeneous nonreacting gas and of an equilibrium mixture of gases consisting of four components (H₂, H₂O, CO, CO₂) are given for different values of the parameters of the main stream and of the blown jet. In the latter case it is assumed that the effect of thermo- and barodiffusion can be neglected.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 55–63, July–August, 1974.     

Asymptotic study of viscous compressible gas flow past a blunt body

Supersonic viscous gas flow past a blunt body is examined. A method is proposed which permits constructing the asymptotic expansion of any order in the small parameter , which characterizes the viscosity and thermal conductivity coefficients. The asymptotic solution is constructed, including terras of zero, first, and second orders of . Acomparison is made with results of other authors who have studied various particular aspects of the subject problem using the method of inner and outer expansions [1–3].     

A class of shear flows of a viscous compressible fluid

Journal of Applied Mechanics and Technical Physics -     

Numerical study of buoyancy- and thermocapillary-driven flows in a cavity

Thermocapillary- and buoyancy-driven convection in open cavities with differentially heated endwalls is investigated by numerical solutions of the two-dimensional Navier-Stokes equations coupled with the energy equation. We studied the thermocapillary and buoyancy convection in the cavities, filled with low-Prandtl-number fluids, with two aspect-ratiosA=1 and 4, Grashof number up to 10⁵ and Reynolds number ⋎Re⋎≤10⁴. Our results show that thermocapillary can have a quite significant effect on the stability of a primarily buoyancy-driven flow, as well as on the flow structures and dynamic behavior for both additive effect (i.e., positiveRe) and opposing effect (i.e., negativeRe).     

Self-similar turbulent compressible gas flows in a channel

In this study we establish for turbulent compressible gas flow (to within a constant factor) the laws governing the variation of the height (radius) and the static pressure along the length of a planar or axisymmetric channel for which the longitudinal velocity component and gas temperature are functions only of the transverse dimensionless coordinate. In such channels the gas density decrease due to friction is compensated by the increase of the cross-sectional area so that the velocity and temperature profiles remain unchanged at all sections of the channel.The results obtained are a generalization to the gas case of the known laws governing the turbulent flow of an incompressible fluid in a cylindrical channel.The author wished to thank A. P. Byrkin for helpful discussions.     

Numerical investigations on vortical structures of viscous film flows along periodic rectangular corrugations

Two-dimensional gravity-driven film flows along a substrate with rectangular corrugations are studied numerically by using Finite Volume Method. The volume of fluid (VOF) method is utilized to capture the evolution of free surfaces. The film flows down an inclined plate are simulated to validate the numerical implementation of the present study. Results obtained indicate that the phase shift between the surface wave and the wall corrugation increases as the Reynolds number. The parametric studies on the interesting resonant phenomenon indicate that the peak Reynolds numbers increase as the raise of the wall depth or the decline of the inclination angle. The dependence of the flow fields is analyzed on the Reynolds numbers and wall depth in details. It is found that the vortical structures in the steady flows, either produced by the interaction between capillary wrinkling and inertia, or by the rectangular geometry, are closely related to the remarkable deformation of the free surfaces. This conclusion is also confirmed by the transient flow development of two typical simulations, i.e., flows in capillary–inertial regime and in inertial regime.     

Calculation of viscous compressible gas flow past a corner

We consider the problem of calculating the parameters for supersonic viscous compressible gas flow past a corner (angle greater than ). The complete system of Navier-Stokes equations for the viscous compressible gas is solved in the small vicinity Q₁. (characteristic dimensionl~1/R) of the corner point. The conditions for smooth matching of the solution of the Navier-Stokes equations and the solution of the ideal gas or boundary layer equations are specified on the boundary of Q₁. All these solutions are a priori unknown, and the conditions for smooth matching reduce to certain differential equations on the boundary of Q₁. Here account is taken of the interaction of the flows near the wall surface and in the so-called outer region [1].We note that no a priori assumptions are made in Q₁ concerning the qualitative behavior of the solution, in contrast with other studies on viscous flow past a corner (for example, [2–4]).The Navier-Stokes system in Q₁ is solved numerically, using the difference scheme suggested in [5]. This scheme permits obtaining the steady-state solution by the asymptotic method for large Reynolds numbers R, and also has an approximation accuracy adequate to account for the effects of low viscosity and thermal conductivity.     

Iterative process acceleration of calculation of unsteady,viscous, compressible,and heat‐conductive gas flows

In this paper, extrapolation technique is introduced in the Semi‐Implicit Method for Pressure‐Linked Equations ‐ Time Step (SIMPLE‐TS) finite volume iterative algorithm for calculation of compressible Navier–Stokes–Fourier equations subject of slip and jump boundary conditions. The initial state, required by the iterative solver in simulation of unsteady flow problems, is approximated in time by Lagrange polynomial extrapolation in each node. The approach is applicable to a parallel code in a straightforward way due to algorithmic independence of the neighboring nodes in the computational grid. A criterion is proposed to determine the order of extrapolation polynomial and stop the extrapolation execution, when the local steady state is reached. The approach is tested on different microflow problems: Couette flow, flow past a square in a microchannel at subsonic and supersonic speeds, and convective Rayleigh–Bénard flow of a rarefied gas. The acceleration varies from 1.14‐fold to 2.8‐fold. Copyright © 2014 John Wiley & Sons, Ltd.     

Some self-similar viscous gas flows in a channel

We consider the class of self-similar axisymmetric and two-dimensional laminar flows of a viscous gas in a long channel with smooth contour, in which the longitudinal component of the velocity and the gas temperature are functions of a single dimensionless transverse coordinate. Such flows correspond to exponential (axisymmetric flow) or linear (two-dimensional flow) increase of the radius or height of the channel and corresponding exponential or hyperbolic decrease of the static pressure along the channel.     

Numerical investigation of unsteady subsonic viscous gas flows in a plane channel with a sudden expansion

The nonlinear processes of development of instability in an unsteady subsonic viscous gas flow in a plane channel with a sudden expansion are investigated numerically with allowance for acoustico-vortex interaction over a broad interval of the characteristic parameters. Effects associated with the acoustic self-excitation of the jet flowing into the wider part of the channel are determined. Approximate relations are obtained for the resonance conditions of self-excitation. The effect of the inlet mean-velocity profiles on the evolution of the flow is estimated. The processes of formation and subsequent interaction of the coherent structures are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 32–41, July–August, 1988.     

Numerical investigation of viscous gas secondary flows in a rotating cylinder with sources and sinks

A source-sink model of secondary flow excitation in a rotating cylinder, which describes the interaction between a circulator and a rotating gas, is proposed for a nonlinear system of Navier-Stokes equations, and the results of a numerical calculation of the resulting circulating flows are presented. The modified Newton's method employed in the numerical solution makes use of regularizing perturbations to ensure its stability and convergence at low Ekman numbers and high rates of rotation of the cylinder. The combined effect of mechanical and thermal means of flow excitation and the influence of viscous energy dissipation are considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 39–44, July–August, 1989.     

On a finite element CFD algorithm for compressible,viscous and turbulent aerodynamic flows

This paper develops and analyses individual construction aspects of an efficient and accurate finite element algorithm for prediction of viscous and turbulent flow fields of impact in aerodynamics. The theoretical construction employs a Taylor weak statement (TWS) for coincident embedding of stability mechanisms within a classic Galerkin finite element formulation of semi-discrete approximation error orthogonalization. A wide variety of the stabilizing mechanisms of independently derived CFD algorithms are contained within the TWS theory. An implicit construction that meets the requirement of efficient convergence to steady state is developed. The theoretical asymptotic error estimates of the TWS finite element algorithm for supersonic and viscous boundary layer flows are verified. Application to a three-dimensional turbulent flow is cited.     

Lp-approach to steady flows of viscous compressible fluids in exterior domains

We investigate steady compressible flows in three-dimensional exterior domains for small data and for both zero and nonzero (but constant) velocity at infinity. We prove existence and uniqueness of solutions in L ^p -spaces, p>3, and study their regularity as well as their decay at infinity.     

Spanwise effects on instabilities of compressible flow over a long rectangular cavity

The stability properties of two-dimensional (2D) and three-dimensional (3D) compressible flows over a rectangular cavity with length-to-depth ratio of \(L/D=6\) are analyzed at a free-stream Mach number of \(M_\infty =0.6\) and depth-based Reynolds number of \(Re_D=502\). In this study, we closely examine the influence of three-dimensionality on the wake mode that has been reported to exhibit high-amplitude fluctuations from the formation and ejection of large-scale spanwise vortices. Direct numerical simulation (DNS) and bi-global stability analysis are utilized to study the stability characteristics of the wake mode. Using the bi-global stability analysis with the time-averaged flow as the base state, we capture the global stability properties of the wake mode at a spanwise wavenumber of \(\beta =0\). To uncover spanwise effects on the 2D wake mode, 3D DNS are performed with cavity width-to-depth ratio of \(W/D=1\) and 2. We find that the 2D wake mode is not present in the 3D cavity flow with \(W/D=2\), in which spanwise structures are observed near the rear region of the cavity. These 3D instabilities are further investigated via bi-global stability analysis for spanwise wavelengths of \(\lambda /D=0.5{-}2.0\) to reveal the eigenspectra of the 3D eigenmodes. Based on the findings of 2D and 3D global stability analysis, we conclude that the absence of the wake mode in 3D rectangular cavity flows is due to the release of kinetic energy from the spanwise vortices to the streamwise vortical structures that develops from the spanwise instabilities.     

Friction characteristics of compressible gas flows in microtubes

The characteristics of a gaseous flow of nitrogen in commercial stainless steel microtubes for gas chromatography having a nominal inner diameter of 762, 508, 254 and 127 μm are experimentally investigated. The friction factor is calculated as a function of the Reynolds number and plotted in a Moody chart. A comparison among three different methods to calculate the friction factor is made in order to evidence limitations and advantages of each method. It was observed that in the laminar regime the Poiseuille law correctly predicts the value of the pressure drop. It has been evidenced that in order to make accurate experiments on the frictional characteristics of commercial microtubes the value of the inner diameter given by the manufacturer has to be always verified. The experimental data presented in this work remark how in microtubes the compressibility effects related to the axial variation of the gas density tend to become important at large Reynolds numbers and small diameters even if the average Mach number is low. The effects due to the gas acceleration on the laminar-to-turbulent transition in microtubes are investigated by evidencing the role of the L/D (length to diameter) ratio on the transition to turbulence. No early transition to turbulence has been evidenced in the tests, instead it takes place at Reynolds numbers ranging between 1800 and 2900.     

Formation of one-dimensional flows of a heat-conducting viscous gas

The article discusses the development of one-dimensional flows in a viscous heat-conducting gas using the example of two flows: 1) the flow arising with the decomposition of a discontinuity of the pressure in the quiescent gas (flow in a shock tube); 2) the flow arising with the application of a constant heat flow at a gassolid interface. For such flows, there has been very little study of the initial stage of the process, right up to the time when nonheat-conducting zones are separated out, described by the Euler equations, as well as dissipation zones of the type of a shock wave or a boundary layer, which can be treated using asymptotic methods [1–3]. With the investigation of the initial stage, the complete solution of the system of Navier—Stokes equations is required. The present article discusses the initial stage of the flows on the basis of a numerical solution of problems 1 and 2. A study is made of the effect of the Prandtl number and of the viscosity coefficient on the behavior of the gas.