A Note On Crossing-trajectory Effects In
Gas-particle Turbulent Flows
Author(s)
B. Oesterl´e
Abstract
In the frame of Lagrangian stochastic dispersion models used to predict the
behaviour of small inertial particles moving in a turbulent flow, crossing-trajectory
effects are generally accounted for by modifying the integral time scales according
to the famous analysis of Csanady (J. Atmos. Sci., 20, pp. 201-208, 1963). Here,
an alternative theoretical analysis of the time correlation of the fluid velocity
fluctuations along a particle trajectory is presented. Analytical expressions of the
integral time scales of the fluid seen by the particles in isotropic turbulence are
first derived in the asymptotic limit where the mean relative velocity is much larger
than the particle velocity fluctuations, then a correction is proposed to extend their
applicability over the whole range of mean relative velocity. These expressions
do not depend on the presumed shape of the two-point fluid velocity correlations.
The predicted time scales in the transverse direction differ from some available
proposals in the literature, but are in agreement with other analyses based on an
assumed functional form of the turbulence spectrum, at least in the limit of large
mean relative velocity.Additionally, some comparisons with numerical predictions
obtained in a synthetic Gaussian turbulence show that the present theoretical
results are in good agreement with the computations in a large range of mean
relative velocity and particle inertia.
Keywords: gas-particle flow, particle dispersion, crossing-trajectory, turbulence.
1 Introduction
As is well known, the behaviour of small inertial particles moving in a turbulent
flow can be described by means of Lagrangian stochastic models that consist in
building a proper stochastic process to predict the instantaneous velocity of the
fluid seen by a discrete particle. The so-called crossing-trajectory effect is observed
when the fluid and particle mean velocities differ due to some external force
Keywords
gas-particle flow, particle dispersion, crossing-trajectory, turbulence.
Related Book
Other papers in this volume
Warning (2)
: foreach() argument must be of type array|object, null given [in
/var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/templates/Papers/view.php, line
364]
Code
$counter = '0';
foreach ($paper['book']['Paper'] as $otherPaper) {
if ((!empty($otherPaper['name'])) && ($counter < '7') && ($otherPaper['available'] == 1)) {
Cake\Error\ErrorTrap->handleError() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/templates/Papers/view.php, line 364
/var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/View/View.php /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/View/View.php, line 1188
Cake\View\View->_evaluate() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/View/View.php, line 1145
Cake\View\View->_render() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/View/View.php, line 785
Cake\View\View->render() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Controller/Controller.php, line 712
Cake\Controller\Controller->render() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Controller/Controller.php, line 516
Cake\Controller\Controller->invokeAction() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Controller/ControllerFactory.php, line 166
Cake\Controller\ControllerFactory->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Controller/ControllerFactory.php, line 141
Cake\Controller\ControllerFactory->invoke() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/BaseApplication.php, line 362
Cake\Http\BaseApplication->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 86
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Middleware/CsrfProtectionMiddleware.php, line 169
Cake\Http\Middleware\CsrfProtectionMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Middleware/BodyParserMiddleware.php, line 157
Cake\Http\Middleware\BodyParserMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Routing/Middleware/RoutingMiddleware.php, line 118
Cake\Routing\Middleware\RoutingMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Routing/Middleware/AssetMiddleware.php, line 69
Cake\Routing\Middleware\AssetMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Error/Middleware/ErrorHandlerMiddleware.php, line 115
Cake\Error\Middleware\ErrorHandlerMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/debug_kit/src/Middleware/DebugKitMiddleware.php, line 60
DebugKit\Middleware\DebugKitMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 60
Cake\Http\Runner->run() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Server.php, line 104
Cake\Http\Server->run() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/webroot/index.php, line 37
[main]
