The influence of entropy fluctuations on the interaction of turbulence with a shock wave

1997 ◽  
Vol 334 ◽  
pp. 353-379 ◽  
Author(s):  
KRISHNAN MAHESH ◽  
SANJIVA K. LELE ◽  
PARVIZ MOIN
Keyword(s):  
Numerical Simulation ◽  
Shock Wave ◽  
Kinetic Energy ◽  
Direct Numerical Simulation ◽  
Scaling Law ◽  
Linear Analysis ◽  
Turbulent Field ◽  
Bulk Compression ◽  
Baroclinic Torque

Direct numerical simulation and inviscid linear analysis are used to study the interaction of a normal shock wave with an isotropic turbulent field of vorticity and entropy fluctuations. The role of the upstream entropy fluctuations is emphasized. The upstream correlation between the vorticity and entropy fluctuations is shown to strongly influence the evolution of the turbulence across the shock. Negative upstream correlation between u′ and T′ is seen to enhance the amplification of the turbulence kinetic energy, vorticity and thermodynamic fluctuations across the shock wave. Positive upstream correlation has a suppressing effect. An explanation based on the relative effects of bulk compression and baroclinic torque is proposed, and a scaling law is derived for the evolution of vorticity fluctuations across the shock. The validity of Morkovin's hypothesis across a shock wave is examined. Linear analysis is used to suggest that shock-front oscillation would invalidate the relation between urms and Trms, as expressed by the hypothesis.

Direct Numerical Simulation of Drops in Three Dimensional Viscoelastic Simple Shear Flows

2001 ◽  
Author(s):  
Shriram B. Pillapakkam ◽  
Pushpendra Singh
Keyword(s):  
Numerical Simulation ◽  
Shear Flow ◽  
Direct Numerical Simulation ◽  
Viscoelastic Fluid ◽  
Simple Shear ◽  
Polymer Concentration ◽  
Three Dimensional ◽  
Simple Shear Flow ◽  
Splitting Technique

Abstract A three dimensional finite element scheme for Direct Numerical Simulation (DNS) of viscoelastic two phase flows is implemented. The scheme uses the Level Set Method to track the interface and the Marchuk-Yanenko operator splitting technique to decouple the difficulties associated with the governing equations. Using this numerical scheme, the shape of Newtonian drops in a simple shear flow of viscoelastic fluid and vice versa are analyzed as a function of Capillary number, Deborah number and polymer concentration. The viscoelastic fluid is modeled via the Oldroyd-B model. The role of viscoelastic stresses in deformation of a drop subjected to simple shear flow and its effect on the steady state shape is analyzed. Our results compare favorably with existing experimental data and also help in understanding the role of viscoelastic stresses in drop deformation.

scholarly journals Direct numerical simulation of conical shock wave–turbulent boundary layer interaction

2019 ◽  
Vol 877 ◽  
pp. 167-195 ◽  
Author(s):  
Feng-Yuan Zuo ◽  
Antonio Memmolo ◽  
Guo-ping Huang ◽  
Sergio Pirozzoli
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Direct Numerical Simulation ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Shear Stresses ◽  
Mean Flow ◽  
Conical Shock

Direct numerical simulation of the Navier–Stokes equations is carried out to investigate the interaction of a conical shock wave with a turbulent boundary layer developing over a flat plate at free-stream Mach number $M_{\infty }=2.05$ and Reynolds number $Re_{\unicode[STIX]{x1D703}}\approx 630$, based on the upstream boundary layer momentum thickness. The shock is generated by a circular cone with half opening angle $\unicode[STIX]{x1D703}_{c}=25^{\circ }$. As found in experiments, the wall pressure exhibits a distinctive N-wave signature, with a sharp peak right past the precursor shock generated at the cone apex, followed by an extended zone with favourable pressure gradient, and terminated by the trailing shock associated with recompression in the wake of the cone. The boundary layer behaviour is strongly affected by the imposed pressure gradient. Streaks are suppressed in adverse pressure gradient (APG) zones, but re-form rapidly in downstream favourable pressure gradient (FPG) zones. Three-dimensional mean flow separation is only observed in the first APG region associated with the formation of a horseshoe vortex, whereas the second APG region features an incipient detachment state, with scattered spots of instantaneous reversed flow. As found in canonical geometrically two-dimensional wedge-generated shock–boundary layer interactions, different amplification of the turbulent stress components is observed through the interacting shock system, with approach to an isotropic state in APG regions, and to a two-component anisotropic state in FPG. The general adequacy of the Boussinesq hypothesis is found to predict the spatial organization of the turbulent shear stresses, although different eddy viscosities should be used for each component, as in tensor eddy-viscosity models, or in full Reynolds stress closures.

scholarly journals The effect of compressibility on turbulent shear flow: a rapid-distortion-theory and direct-numerical-simulation study

1997 ◽  
Vol 330 ◽  
pp. 307-338 ◽  
Author(s):  
A. SIMONE ◽  
G.N. COLEMAN ◽  
C. CAMBON
Keyword(s):  
Numerical Simulation ◽  
Mach Number ◽  
Kinetic Energy ◽  
Shear Flow ◽  
Direct Numerical Simulation ◽  
Pure Shear ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Rapid Distortion Theory ◽  
The Mean

The influence of compressibility upon the structure of homogeneous sheared turbulence is investigated. For the case in which the rate of shear is much larger than the rate of nonlinear interactions of the turbulence, the modification caused by compressibility to the amplification of turbulent kinetic energy by the mean shear is found to be primarily reflected in pressure–strain correlations and related to the anisotropy of the Reynolds stress tensor, rather than in explicit dilatational terms such as the pressure–dilatation correlation or the dilatational dissipation. The central role of a ‘distortion Mach number’ Md =  S[lscr ]/a, where S is the mean strain or shear rate, [lscr ] a lengthscale of energetic structures, and a the sonic speed, is demonstrated. This parameter has appeared in previous rapid-distortion-theory (RDT) and direct-numerical-simulation (DNS) studies; in order to generalize the previous analyses, the quasi-isentropic compressible RDT equations are numerically solved for homogeneous turbulence subjected to spherical (isotropic) compression, one-dimensional (axial) compression and pure shear. For pure-shear flow at finite Mach number, the RDT results display qualitatively different behaviour at large and small non-dimensional times St: when St < 4 the kinetic energy growth rate increases as the distortion Mach number increases; for St > 4 the inverse occurs, which is consistent with the frequently observed tendency for compressibility to stabilize a turbulent shear flow. This ‘crossover’ behaviour, which is not present when the mean distortion is irrotational, is due to the kinematic distortion and the mean-shear-induced linear coupling of the dilatational and solenoidal fields. The relevance of the RDT is illustrated by comparison to the recent DNS results of Sarkar (1995), as well as new DNS data, both of which were obtained by solving the fully nonlinear compressible Navier–Stokes equations. The linear quasi-isentropic RDT and nonlinear non-isentropic DNS solutions are in good general agreement over a wide range of parameters; this agreement gives new insight into the stabilizing and destabilizing effects of compressibility, and reveals the extent to which linear processes are responsible for modifying the structure of compressible turbulence.

Direct Numerical Simulation and RANS Modeling of Turbulent Natural Convection for Low Prandtl Number Fluids

2004 ◽  
Author(s):  
I. Otic´ ◽  
G. Gro¨tzbach
Keyword(s):  
Numerical Simulation ◽  
Heat Flux ◽  
Kinetic Energy ◽  
Prandtl Number ◽  
Direct Numerical Simulation ◽  
Turbulent Heat Flux ◽  
Turbulent Heat ◽  
Temperature Variance ◽  
Flux Model ◽  
Heat Flux Model

Results of direct numerical simulation (DNS) of turbulent Rayleigh-Be´nard convection for a Prandtl number Pr = 0.025 and a Rayleigh number Ra = 105 are used to evaluate the turbulent heat flux and the temperature variance. The DNS evaluated turbulent heat flux is compared with the DNS based results of a standard gradient diffusion turbulent heat flux model and with the DNS based results of a standard algebraic turbulent heat flux model. The influence of the turbulence time scales on the predictions by the standard algebraic heat flux model at these Rayleigh- and Prandtl numbers is investigated. A four equation algebraic turbulent heat flux model based on the transport equations for the turbulent kinetic energy k, for the dissipation of the turbulent kinetic energy ε, for the temperature variance θ2, and for the temperature variance dissipation rate εθ is proposed. This model should be applicable to a wide range of low Prandtl number flows.

Direct Numerical Simulation of Radial Convection in a Cylindrical Annulus With and Without Rotation

2019 ◽  
Author(s):  
Diogo B. Pitz ◽  
William R. Wolf
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Nusselt Number ◽  
Kinetic Energy ◽  
Direct Numerical Simulation ◽  
Centrifugal Acceleration ◽  
Radial Acceleration ◽  
Turbulent Fluctuations ◽  
Parallel Disks ◽  
Cylindrical Annulus

Abstract In rotating systems with temperature gradients, convection may occur due to gravitational or centrifugal effects. In cases where rotation is strong enough so that the centrifugal acceleration is higher than gravity, the flow is induced by centrifugal buoyancy and gravitational effects can be neglected. The problem of flow induced by centrifugal buoyancy in a cylindrical annulus has been used as a canonical setup to investigate industrial configurations, such as buoyancy-driven flows occurring in gas turbine secondary air systems, as well as geophysical flows, such as convection in the core of planets and the global circulation of the atmosphere. Due to the constraints imposed by the Taylor-Proudman theorem, such flows are quasi-homogeneous along the axial direction, and heat transfer as well as turbulent fluctuations tend to be suppressed by the action of the Coriolis force. Previous work has demonstrated that when the annulus is bounded by parallel disks, boundary layers scaling consistently with laminar Ekman layers are formed near each of the disks, even though the flow is purely buoyancy-induced. Also, the Nusselt number measured on the outer cylindrical surface has been shown to scale with the Rayleigh number as in natural convection between horizontal plates. In the present work we use direct numerical simulation (DNS) to investigate buoyancy-induced flow in an air-filled cylindrical annulus bounded by two adiabatic parallel disks, with and without rotation around the axis. In both cases the outer cylindrical surface is at a higher temperature than the inner one, so that a radial acceleration directed outwards induces an unstable stratification. In the case with rotation, the flow is induced by the centrifugal acceleration in the radial direction, and Coriolis forces are considered. For the case without rotation, the Coriolis terms are suppressed in the calculations, whereas the radial acceleration is the same as in the rotating case. Statistics are obtained and compared in the two cases, including the time-averaged Nusselt number, mean temperature profiles, velocity and temperature fluctuations, as well as terms of the turbulent kinetic energy equation. By analysing such statistics, the extent to which rotation suppresses heat transfer and turbulent fluctuations, as well as the contribution of each term to the turbulent kinetic energy budget, can be assessed.

0802 Validation of Interaction between Multiple Particles and Shock Wave by Direct Numerical Simulation

2015 ◽  
Vol 2015 (0) ◽  
pp. _0802-1_-_0802-4_
Author(s):  
Yusuke Mizuno ◽  
Shun Takahashi ◽  
Taku Nonomura ◽  
Takayuki Nagata ◽  
Kota Fukuda
Keyword(s):  
Numerical Simulation ◽  
Shock Wave ◽  
Direct Numerical Simulation ◽  
Multiple Particles

The Analysis of Direct Numerical Simulation and Experiment in Critical Point of Transitional Flow

2014 ◽  
Vol 1046 ◽  
pp. 196-199
Author(s):  
Jun Wang ◽  
Guang Sheng Du ◽  
Yong Hui Liu
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Critical Point ◽  
Transitional Flow ◽  
Viscous Force ◽  
Wall Region ◽  
Flow State ◽  
Transitional Area ◽  
Simulation And Experiment

In order to study the lower critical point in transitional area of pipe, we used the method of direct numerical simulation to simulate fluid flow and contrasted it with experiment. The result showed that the flow state is close to laminar. Along the pipe axis, the change of pressure is not obviously. The changing rate of axial velocity U near wall region was significantly greater than in the mainstream area, it proved the important role of viscous force.

Direct numerical simulation of isotropic turbulence interacting with a weak shock wave

1993 ◽  
Vol 251 ◽  
pp. 533-562 ◽  
Author(s):  
Sangsan Lee ◽  
Sanjiva K. Lele ◽  
Parviz Moin
Keyword(s):  
Shock Wave ◽  
Kinetic Energy ◽  
Shock Waves ◽  
Shock Front ◽  
Numerical Simulations ◽  
Turbulent Kinetic Energy ◽  
Isotropic Turbulence ◽  
Weak Shock ◽  
Linear Analysis ◽  
Weak Shock Wave

Interaction of isotropic quasi-incompressible turbulence with a weak shock wave was studied by direct numerical simulations. The effects of the fluctuation Mach number Mt of the upstream turbulence and the shock strength M21 — 1 on the turbulence statistics were investigated. The ranges investigated were 0.0567 ≤ Mt ≤ 0.110 and 1.05 ≤ M1 ≤ 1.20. A linear analysis of the interaction of isotropic turbulence with a normal shock wave was adopted for comparisons with the simulations.Both numerical simulations and the linear analysis of the interaction show that turbulence is enhanced during the interaction with a shock wave. Turbulent kinetic energy and transverse vorticity components are amplified, and turbulent lengthscales are decreased. The predictions of the linear analysis compare favourably with simulation results for flows with M2t < a(M21 — 1) with a ≈ 0.1, which suggests that the amplification mechanism is primarily linear. Simulations also showed a rapid evolution of turbulent kinetic energy just downstream of the shock, a behaviour not reproduced by the linear analysis. Investigation of the budget of the turbulent kinetic energy transport equation shows that this behaviour can be attributed to the pressure transport term.Shock waves were found to be distorted by the upstream turbulence, but still had a well-defined shock front for M2t < a(M21— 1) with a ≈ 0.1). In this regime, the statistics of shock front distortions compare favourably with the linear analysis predictions. For flows with M2t > a(M21— 1 with a ≈ 0.1, shock waves no longer had well-defined fronts: shock wave thickness and strength varied widely along the transverse directions. Multiple compression peaks were found along the mean streamlines at locations where the local shock thickness had increased significantly.

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