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Analysis of periodically-forced turbulence in the rapid distortion limitO'Neil, Joshua Robert 12 April 2006 (has links)
Rapid Distortion Theory is used to perform calculations of unsteadily-forced initially
isotropic turbulence so that the physics of such flows can be better understood. The
results of these calculations show that there are three distinct regimes of physical behavior
for the kind of turbulence that we are considering: (1) turbulence that is forced
at a relatively low frequency in which the kinetic energy settles down to a constant
value at later times, (2) turbulence that is forced at a slightly higher frequency in
which the kinetic energy value oscillates for a time, but then increases dramatically,
and (3) turbulence that is forced at a relatively high frequency in which the kinetic
energy evolution exhibits a periodic behavior. To better understand the role of the
rapid pressure-strain correlation, these results are also compared to Inertial Model
results for the same set of forcing frequencies. The results of this comparison show
that the rapid pressure plays a key role in determining the stability characteristics of
unsteadily-forced turbulence. The evolution equation for kinetic energy is then used
to propose a model that describes the behavior approximately in terms of a time lag
between applied mean strain and the Reynolds stress. This model suggests that the
different responses under the different frequencies of forcing correspond to different
stress-strain time lags. Overall, then the results indicate that rapid pressure serves to
create a time lag between applied stress and strain, and it is the extent of this time
lag that causes turbulence to respond differently under various frequencies of forcing.
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Turbulence Interaction in a Highly Sataggered Cascade-Propulsor Configurationde la Riva, Diego Horacio 01 May 2001 (has links)
Measurements of the turbulent flow field through a highly staggered cascade propulsor configuration in the Virginia Tech cascade wind tunnel have been taken. Predictions of the same flow using Rapid Distortion Theory (RDT) were performed. Measurements and predictions were compared. The comparison was oriented to check the aptness of RDT in describing this kind of flow.
Since this study represents the initial steps of a major project, the RDT model was kept simple. The non-penetration condition (blade blocking effect) was not modeled and the viscous effects were roughly accounted for.
This work reveals the capabilities of RDT in predicting the development of turbulence convected through a highly staggered cascade propulsor configuration formed by non-symmetrical airfoils.
This present study was possible thank to the support from the Office of Naval Research, in particular Candace Wark and Pat Purtell, under grant number NAG 00014-99-1-0230. / Master of Science
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Rapidly Sheared Compressible Turbulence: Characterization of Different Pressure Regimes and Effect of Thermodynamic FluctuationsBertsch, Rebecca Lynne 2010 August 1900 (has links)
Rapid distortion theory (RDT) is applied to compressible ideal-gas turbulence subjected to homogeneous shear flow. The study examines the linear or rapid processes present in turbulence evolution. Specific areas of investigation include:(i) characterization of the multi-stage flow behavior,(ii) changing role of pressure in the three-regime evolution and (iii) influence of thermodynamic fluctuations on the different regimes. Preliminary investigations utilizing the more accurate Favre-averaged RDT approach show promise however, this approach requires careful validation and testing. In this study the Favre-averaged RDT approach is validated against Direct Numerical Simulation (DNS) and Reynolds-averaged RDT results. The three-stage growth of the flow field statistics is first confirmed. The three regime evolution of turbulence is then examined in three different timescales and the physics associated with each regime is discussed in depth. The changing role of pressure in compressible turbulence evolution shows three distinct stages. The physics of each stage is clearly explained. Next, the influence of initial velocity and thermodynamic fluctuations on the flow field are investigated. The evolution of turbulence is shown to be strongly dependent on the initial gradient Mach number and initial temperature fluctuations which tend to delay the onset of the second regime of evolution. The initial turbulent Mach number, which quantifies velocity fluctuations in the flow, influences turbulence evolution only weakly. Comparison of Reynolds-averaged RDT against Favre-averaged RDT for simulations of nonzero initial flow field fluctuations shows the higher fidelity of the latter approach.
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Charecterization of inertial and pressure effects in homogeneous turbulenceBikkani, Ravi Kiran 01 November 2005 (has links)
The objective of the thesis is to characterize the linear and nonlinear aspects of inertial
and pressure effects in turbulent flows. In the first part of the study, computations of
Navier-Stokes and 3D Burgers equations are performed in the rapid distortion (RD) limit
to analyze the inviscid linear processes in homogeneous turbulence. By contrasting the
results of Navier- Stokes RD equations and Burgers RD equations, the effect of pressure
can be isolated. The evolution of turbulent kinetic energy and anisotropy components
and invariants are examined. In the second part of the thesis, the velocity gradient
dynamics in turbulent flows are studied with the help of inviscid 3D Burgers equations
and restricted Euler equations. The analytical asymptotic solutions of velocity gradient
tensor are obtained for both Burgers and restricted Euler equations. Numerical
computations are also performed to identify the stable solutions. The results are
compared and contrasted to identify the effect of pressure on nonlinear velocity gradient
dynamics. Of particular interest are the sign of the intermediate principle strain-rate and
tendency of vorticity to align with the intermediate principle strain-rate. These aspects of
velocity gradients provide valuable insight into the role of pressure in the energy cascade
process.
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Reynolds and Favre-averaged rapid distortion theory for compressible, ideal-gas turbulenceLavin, Tucker Alan 17 September 2007 (has links)
Compressible ideal-gas turbulence subjected to homogeneous shear is investigated
at the rapid distortion limit. Specific issues addressed are (i) the interaction
between kinetic and internal energies and role of pressure-dilatation; (ii) the modifications
to pressure-strain correlation and Reynolds stress anisotropy and (iii) the effect
of the composition of velocity fluctuations (solenoidal vs. dilatational). Turbulence
evolution is found to be strongly influenced by gradient Mach number, the initial
solenoidal-to-dilatational ratio of the velocity field and the initial intensity of the
thermodynamic fluctuations. The balance between the initial fluctuations in velocity
and thermodynamic variables is also found to be very important. Any imbalance
in the two fluctuating fields leads to high levels of pressure-dilatation and intense
exchange.
For a given initial condition, it is found that the interaction via the pressuredilatation
term between the momentum and energy equations reaches a peak at an
intermediate gradient Mach number. The energy exchange between internal and kinetic
modes is negligible at very high or very low Mach number values due to lack of
pressure dilatation. When present, the exchange exhibits oscillations even as the sum
of the two energies evolves smoothly. The interaction between shear and solenoidal
initial velocity field generates dilatational fluctuations; for some intermediate levels of
shear Mach number dilatational fluctuations account for 20% of the total fluctuations.
Similarly, the interaction between shear and initial dilatation produces solenoidal oscillations. Somewhat surprisingly, the generation of solenoidal fluctuations increases
with gradient Mach number. Larger levels of pressure-strain correlation are seen with
dilatational rather than solenoidal initial conditions. Anisotropies of solenoidal and
dilatational components are investigated individually. The most interesting observation
is that solenoidal and dilatational turbulence tend toward a one componential
state but the energetic component is different in each case. As in incompressible shear
flows, with solenoidal fluctuations, the streamwise (1,1) component of Reynolds stress
is dominant. With dilatational fluctuations, the stream-normal (2,2) component is
the strongest. Overall, the study yields valuable insight into the linear processes in
high Mach number shear flows and identifies important closure modeling issues.
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A Dynamical Systems Approach Towards Modeling the Rapid Pressure Strain CorrelationMishra, Aashwin A. 2010 May 1900 (has links)
In this study, the behavior of pressure in the Rapid Distortion Limit, along with its
concomitant modeling, are addressed. In the first part of the work, the role of pressure in
the initiation, propagation and suppression of flow instabilities for quadratic flows is
analyzed. The paradigm of analysis considers the Reynolds stress transport equations to
govern the evolution of a dynamical system, in a state space composed of the Reynolds
stress tensor components. This dynamical system is scrutinized via the identification of
the invariant sets and the bifurcation analysis. The changing role of pressure in quadratic
flows, viz. hyperbolic, shear and elliptic, is established mathematically and the
underlying physics is explained. Along the maxim of "understanding before prediction", this allows for a deeper insight into the behavior of pressure, thus aiding in its modeling.
The second part of this work deals with Rapid Pressure Strain Correlation modeling in
earnest. Based on the comprehension developed in the preceding section, the classical
pressure strain correlation modeling approaches are revisited. Their shortcomings, along
with their successes, are articulated and explained, mathematically and from the
viewpoint of the governing physics. Some of the salient issues addressed include, but are not limited to, the requisite nature of the model, viz. a linear or a nonlinear structure,
the success of the extant models for hyperbolic flows, their inability to capture elliptic
flows and the use of RDT simulations to validate models. Through this analysis, the
schism between mathematical and physical guidelines and the engineering approach, at
present, is substantiated. Subsequently, a model is developed that adheres to the classical
modeling framework and shows excellent agreement with the RDT simulations. The
performance of this model is compared to that of other nominations prevalent in
engineering simulations. The work concludes with a summary, pertinent observations
and recommendations for future research in the germane field.
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Selected problems in turbulence theory and modelingJeong, Eun-Hwan 30 September 2004 (has links)
Three different topics of turbulence research that cover modeling, theory and model computation categories are selected and studied in depth. In the first topic, "velocity gradient dynamics in turbulence" (modeling), the Lagrangian linear diffusion model that accounts for the viscous-effect is proposed to make the existing restricted-Euler velocity gradient dynamics model quantitatively useful. Results show good agreement with DNS data. In the second topic, "pressure-strain correlation in homogeneous anisotropic turbulence subject to rapid strain-dominated distortion" (theory), extensive rapid distortion calculation is performed for various anisotropic initial turbulence conditions in strain-dominated mean flows. The behavior of the rapid pressure-strain correlation is investigated and constraining criteria for the rapid pressure-strain correlation models are developed. In the last topic, "unsteady computation of turbulent flow past a square cylinder using partially-averaged Navier-Stokes method" (model computation), the basic philosophy of the PANS method is reviewed and a practical problem of flow past a square cylinder is computed for various levels of physical resolution. It is revealed that the PANS method can capture many important unsteady flow features at an affordable computational effort.
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Selected problems in turbulence theory and modelingJeong, Eun-Hwan 30 September 2004 (has links)
Three different topics of turbulence research that cover modeling, theory and model computation categories are selected and studied in depth. In the first topic, "velocity gradient dynamics in turbulence" (modeling), the Lagrangian linear diffusion model that accounts for the viscous-effect is proposed to make the existing restricted-Euler velocity gradient dynamics model quantitatively useful. Results show good agreement with DNS data. In the second topic, "pressure-strain correlation in homogeneous anisotropic turbulence subject to rapid strain-dominated distortion" (theory), extensive rapid distortion calculation is performed for various anisotropic initial turbulence conditions in strain-dominated mean flows. The behavior of the rapid pressure-strain correlation is investigated and constraining criteria for the rapid pressure-strain correlation models are developed. In the last topic, "unsteady computation of turbulent flow past a square cylinder using partially-averaged Navier-Stokes method" (model computation), the basic philosophy of the PANS method is reviewed and a practical problem of flow past a square cylinder is computed for various levels of physical resolution. It is revealed that the PANS method can capture many important unsteady flow features at an affordable computational effort.
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