Finite Time Correlations and Compressibility Effects in the Three-Dimensional Kraichnan Model

Using the field theoretic renormalization group technique the simultaneous influence of the compressibility and finite time correlations of the non-solenoidal Gaussian velocity field on the advection of a passive scalar field is studied within the generalized Kraichnan model in three spatial dimensions up to the second-order approximation in the corresponding perturbative expansion. All possible infrared stable fixed points of the model, which drive the corresponding scaling regimes of the model, are identified and their regions of the infrared stability in the model parametric space are discussed. It is shown that, depending on the value of the parameter that drives the compressibility of the system, there exists a gap in the parametric space between the regions where the model with the frozen velocity field and the model with finite-time correlations of the velocity field are stable or there exists an overlap between them.

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Anomalous scaling in the Kazantsev-Kraichnan model with finite time correlations: two-loop renormalization group analysis of relevant composite operators

The European Physical Journal B ◽

10.1140/epjb/e2018-90511-0 ◽

2018 ◽

Vol 91 (12) ◽

Cited By ~ 3

Author(s):

Eva Jurčišinová ◽

Marian Jurčišin ◽

Martin Menkyna

Keyword(s):

Renormalization Group ◽

Finite Time ◽

Group Analysis ◽

Anomalous Scaling ◽

Renormalization Group Analysis ◽

Kraichnan Model ◽

Time Correlations

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Influence of compressibility on scaling regimes of Kraichnan model with finite time correlations: two-loop RG analysis

The European Physical Journal B ◽

10.1140/epjb/e2020-100484-0 ◽

2020 ◽

Vol 93 (4) ◽

Author(s):

Martin Menkyna

Keyword(s):

Finite Time ◽

Kraichnan Model ◽

Time Correlations

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Cascades of temperature and entropy fluctuations in compressible turbulence

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.116 ◽

2019 ◽

Vol 867 ◽

pp. 195-215 ◽

Cited By ~ 12

Author(s):

Jianchun Wang ◽

Minping Wan ◽

Song Chen ◽

Chenyue Xie ◽

Lian-Ping Wang ◽

...

Keyword(s):

Velocity Field ◽

Velocity Component ◽

Three Dimensional ◽

Passive Scalar ◽

Inertial Range ◽

Compressible Turbulence ◽

Equilibrium Relation ◽

Geometrical Properties ◽

Conditional Averaging ◽

Incompressible Turbulence

Cascades of temperature and entropy fluctuations are studied by numerical simulations of stationary three-dimensional compressible turbulence with a heat source. The fluctuation spectra of velocity, compressible velocity component, density and pressure exhibit the $-5/3$ scaling in an inertial range. The strong acoustic equilibrium relation between spectra of the compressible velocity component and pressure is observed. The $-5/3$ scaling behaviour is also identified for the fluctuation spectra of temperature and entropy, with the Obukhov–Corrsin constants close to that of a passive scalar spectrum. It is shown by Kovasznay decomposition that the dynamics of the temperature field is dominated by the entropic mode. The average subgrid-scale (SGS) fluxes of temperature and entropy normalized by the total dissipation rates are close to 1 in the inertial range. The cascade of temperature is dominated by the compressible mode of the velocity field, indicating that the theory of a passive scalar in incompressible turbulence is not suitable to describe the inter-scale transfer of temperature in compressible turbulence. In contrast, the cascade of entropy is dominated by the solenoidal mode of the velocity field. The different behaviours of cascades of temperature and entropy are partly explained by the geometrical properties of SGS fluxes. Moreover, the different effects of local compressibility on the SGS fluxes of temperature and entropy are investigated by conditional averaging with respect to the filtered dilatation, demonstrating that the effect of compressibility on the cascade of temperature is much stronger than on the cascade of entropy.

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On a class of unsteady three-dimensional Navier—Stokes solutions relevant to rotating disc flows: threshold amplitudes and finite-time singularities

Journal of Fluid Mechanics ◽

10.1017/s0022112092001721 ◽

1992 ◽

Vol 238 ◽

pp. 297-323 ◽

Cited By ~ 8

Author(s):

Philip Hall ◽

P. Balakumar ◽

D. Papageorgiu

Keyword(s):

Exact Solution ◽

Velocity Field ◽

Continuous Spectrum ◽

Stagnation Point ◽

Finite Time ◽

Stokes Equations ◽

Three Dimensional ◽

Stagnation Point Flow ◽

Navier Stokes ◽

Rotating Disc

A class of ‘exact’ steady and unsteady solutions of the Navier—Stokes equations in cylindrical polar coordinates is given. The flows correspond to the motion induced by an infinite disc rotating in the (x, y)-plane with constant angular velocity about the z-axis in a fluid occupying a semi-infinite region which, at large distances from the disc, has velocity field proportional to (x, — y,O) with respect to a Cartesian coordinate system. It is shown that when the rate of rotation is large Kármán's exact solution for a disc rotating in an otherwise motionless fluid is recovered. In the limit of zero rotation rate a particular form of Howarth's exact solution for three-dimensional stagnation-point flow is obtained. The unsteady form of the partial differential system describing this class of flow may be generalized to time-periodic flows. In addition the unsteady equations are shown to describe a strongly nonlinear instability of Kármán's rotating disc flow. It is shown that sufficiently large perturbations lead to a finite-time breakdown of that flow whilst smaller disturbances decay to zero. If the stagnation point flow at infinity is sufficiently strong the steady basic states become linearly unstable. In fact there is then a continuous spectrum of unstable eigenvalues of the stability equations but, if the initial-value problem is considered, it is found that, at large values of time, the continuous spectrum leads to a velocity field growing exponentially in time with an amplitude decaying algebraically in time.

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Momentum and heat transport in a three-dimensional transitional wake of a heated square cylinder

Journal of Fluid Mechanics ◽

10.1017/s0022112009991285 ◽

2009 ◽

Vol 640 ◽

pp. 109-129 ◽

Cited By ~ 15

Author(s):

L. DJENIDI ◽

R. A. ANTONIA

Keyword(s):

Spatial Organization ◽

Transport Model ◽

Order Approximation ◽

Three Dimensional ◽

Passive Scalar ◽

Wake Flow ◽

Square Cylinder ◽

Reynolds Analogy ◽

First Order Approximation ◽

Boltzmann Method

The transport of momentum and a passive scalar (temperature) in a three-dimensional transitional wake of a heated square cylinder has been carried out through direct numerical simulations using the lattice Boltzmann method at a Reynolds number Rd = 200 (d is the cylinder diameter) and a Prandlt number of 0.7. The simulations shows that while momentum and heat are transported by vortical structures, heat is in general more effectively transported than momentum. It is argued that the nature of the structural flow is responsible for the longitudinal heat flux uθ being larger than the lateral one vθ in the wake region extending up to 45d. It was shown that a gradient transport model could, to a first-order approximation, be used to model uv but would be less accurate for modelling vθ. Also the Reynolds analogy between momentum and heat transports is not verified in this flow. The fluctuating temperature field presents thermal structures similar to the velocity structures with, however, a different spatial organization. In addition the analogy between fluctuating turbulent kinetic energy and the temperature variance is relatively well satisfied throughout the wake flow.

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Design of finite-time guidance law based on observer and head-pursuit theory

Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering ◽

10.1177/0954410020984562 ◽

2021 ◽

pp. 095441002098456

Author(s):

Chenqi Zhu

Keyword(s):

Finite Time ◽

Three Dimensional ◽

Hypersonic Vehicle ◽

Two Dimensional ◽

Dimensional Model ◽

Reaching Law ◽

Guidance Law ◽

Fast Power ◽

Simulation Results ◽

Guidance Laws

In order to improve the guiding accuracy in intercepting the hypersonic vehicle, this article presents a finite-time guidance law based on the observer and head-pursuit theory. First, based on a two-dimensional model between the interceptor and target, this study applies the fast power reaching law to head-pursuit guidance law so that it can alleviate the chattering phenomenon and ensure the convergence speed. Second, target maneuvers are considered as system disturbances, and the head-pursuit guidance law based on an observer is proposed. Furthermore, this method is extended to a three-dimensional case. Finally, comparative simulation results further verify the superiority of the guidance laws designed in this article.

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A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽

10.3390/math9070756 ◽

2021 ◽

Vol 9 (7) ◽

pp. 756

Author(s):

Federico Lluesma-Rodríguez ◽

Francisco Álcantara-Ávila ◽

María Jezabel Pérez-Quiles ◽

Sergio Hoyas

Keyword(s):

Heat Transfer ◽

Stokes Equations ◽

Three Dimensional ◽

Turbulent Channel Flow ◽

Passive Scalar ◽

Direct Numerical Simulations ◽

Time Dependent ◽

Navier Stokes ◽

Thermal Flow ◽

Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

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Optimization of the Three-Dimensional Flow Path in the Scroll-Nozzle System of a Radial Inflow Turbine

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.3239600 ◽

1984 ◽

Vol 106 (2) ◽

pp. 511-515 ◽

Cited By ~ 1

Author(s):

E. A. Baskharone

Keyword(s):

Flow Analysis ◽

Three Dimensional ◽

Inviscid Flow ◽

Three Dimensional Flow ◽

Multiply Connected ◽

Dimensional Flow ◽

Nozzle Configuration ◽

Flow Domain ◽

Radial Inflow Turbine ◽

Compressibility Effects

A three-dimensional inviscid flow analysis in the combined scroll-nozzle system of a radial inflow turbine is presented. The coupling of the two turbine components leads to a geometrically complicated, multiply-connected flow domain. Nevertheless, this coupling accounts for the mutual effects of both elements on the three-dimensional flow pattern throughout the entire system. Compressibility effects are treated for an accurate prediction of the nozzle performance. Different geometrical configurations of both the scroll passage and the nozzle region are investigated for optimum performance. The results corresponding to a sample scroll-nozzle configuration are verified by experimental measurements.

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