Shock–turbulence interactions at high turbulence intensities

2019 ◽  
Vol 870 ◽  
pp. 813-847 ◽  
Author(s):  
Chang Hsin Chen ◽  
Diego A. Donzis
Keyword(s):  
Quasi Equilibrium ◽  
Weak Turbulence ◽  
Incoming Flow ◽  
Strong Turbulence ◽  
High Turbulence ◽  
Thermodynamic Variables ◽  
Forcing Mechanisms ◽  
Reynolds Number Dependence ◽  
Theoretical Results ◽  
Universal Behaviour

Shock–turbulence interactions are investigated using well-resolved direct numerical simulations (DNS) and analysis at a range of Reynolds, mean and turbulent Mach numbers ($R_{\unicode[STIX]{x1D706}}$, $M$ and $M_{t}$, respectively). The simulations are shock and turbulence resolving with $R_{\unicode[STIX]{x1D706}}$ up to 65, $M_{t}$ up to 0.54 and $M$ up to 1.4. The focus is on the effect of strong turbulence on the jumps of mean thermodynamic variables across the shock, the shock structure and the amplification of turbulence as it moves through the shock. Theoretical results under the so-called quasi-equilibrium (QE) assumption provide explicit laws for a number of statistics of interests which are in agreement with the new DNS data presented here as well as all the data available in the literature. While in previous studies turbulence was found to weaken jumps, it is shown here that stronger jumps are also observed depending on the regime of the interaction. Statistics of the dilatation at the shock are also investigated and found to be well represented by QE for weak turbulence but saturate at high turbulence intensities with a Reynolds number dependence also captured by the analysis. Finally, amplification factors are found to present a universal behaviour with two limiting asymptotic regimes governed by $(M-1)$ and $K=M_{t}/R_{\unicode[STIX]{x1D706}}^{1/2}(M-1)$, for weak and strong turbulence, respectively. Effect of anisotropy in the incoming flow is also assessed by utilizing two different forcing mechanisms to generate turbulence.

Explanation of the Influence of Inflow Air Content on the Lift of Cavitating Hydrofoils

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Eduard Amromin
Keyword(s):  
Experimental Data ◽  
Theoretical Study ◽  
Lift Coefficient ◽  
Cavity Surface ◽  
Air Bubbles ◽  
Incoming Flow ◽  
Fluid Density ◽  
Air Content ◽  
Theoretical Results ◽  
Good Agreement

According to several known experiments, an increase of the incoming flow air content can increase the hydrofoil lift coefficient. The presented theoretical study shows that such increase is associated with the decrease of the fluid density at the cavity surface. This decrease is caused by entrainment of air bubbles to the cavity from the surrounding flow. The theoretical results based on such explanation are in a good agreement with the earlier published experimental data for NACA0015.

Power Output Efficiency in Large Wind Farms with Different Streamwise Turbine Spacing

2020 ◽  
Author(s):  
Yu-Ting Wu ◽  
Yu-Hsiang Tsao
Keyword(s):  
Power Output ◽  
Wind Farm ◽  
Wind Farms ◽  
Power Production ◽  
Internal Boundary ◽  
Incoming Flow ◽  
Flow Conditions ◽  
Inflow Condition ◽  
High Turbulence ◽  
Large Wind

<p>A large-eddy simulation (LES) model, coupled with a dynamic actuator-disk model, is used to investigate the turbine power production and the turbine wake distribution in large wind farms where the streamwise turbine spacing of 7, 9, 12, 15, and 18 rotor diameters are considered. Two incoming flow conditions, three wind turbine arrangements, as well as the five turbine spacings are involved in this study, which leads to a total of 30 LES wind farm scenarios. The two incoming flow conditions have the same mean velocity of 9 m s<sup>-1</sup> but different turbulence intensity levels (i.e., 7% and 11%) at the hub height level. The considered turbine arrangements are the perfectly-aligned, laterally-staggered, and vertically-staggered layouts. The simulated results show that the turbine power production has a significant improvement by increasing the streamwise turbine spacing. With increasing the streamwise turbine spacing from 7 to 18 rotor diameters, the overall averaged power outputs are raised by about 27% in the staggered wind farms and about 38% in the aligned wind farms. The wind farm scenarios with the turbine spacing of 12d or greater in a large wind farm can lead to an increasing trend in the power production from the downstream turbines in the high-turbulence inflow condition, or also avoids the degradation of the power output on the turbines with the low-turbulence inflow condition. The flow adjustment above the wind farm results in the generation of the internal boundary layer (IBL), which grows up vertically along with the wake-wise direction. The growth of the IBL is found to be affected by the changes in the inflow condition and the turbine spacing. The IBL depth above the wind farms is found to be influenced by the turbine spacing, whereas the IBL depth in the downstream wake region of the wind farms shows a rapid increase under the high-turbulence inflow condition.</p>

scholarly journals Mixing and Transport in Stars

2002 ◽  
Vol 12 ◽  
pp. 295-297
Author(s):  
Vittorio M. Canuto
Keyword(s):  
Convective Zone ◽  
Considerable Progress ◽  
Weak Turbulence ◽  
Dynamical Processes ◽  
Unstable Stratification ◽  
Strong Turbulence ◽  
Stellar Interiors ◽  
Transport And Mixing ◽  
Different Origin ◽  
Mixing And Transport

Transport and mixing in stars is as important as it is difficult to quantify (Zahn 1992; Schatzman 1996; Maeder 1997; Pinsonneault 1997). A first difficulty is that both transport and mixing are dynamical processes which, given the low viscosities of stellar interiors, usually means that the flow is turbulent giving rise to technical difficulties for turbulence is still an incomplete chapter though recent studies have brought about considerable progress. A second difficulty is that turbulence is not self-sustaining and unless there is a source, dynamical mixing and transport will decay in time and eventually die out. Thus, the question: what is the source of turbulence, let alone how to describe it? In the convective zone, the source is the unstable stratification but the mixing there is so strong that one does not need a sophisticated theory to describe it. Strong turbulence is easier to describe than weak turbulence and yet the latter is when the problems become interesting and our descriptive power is less reliable. For example, below the solar CZ we don’t even know for sure the source of stirring, let alone how to describe it and yet, it is the region where we would like to be confident about models. The transport of Li is the best example of a mixing and transport that cannot be too strong or too weak (Schlattl and Weiss 1999). A third difficulty is the unstated assumption that “transport” (advection) and “mixing” (diffusion) have different origin.

Diffusion via native defects, and the appropriate choice of independent thermodynamic variables in both quasi-equilibrium and nonequilibrium experimental designs

1997 ◽  
Vol 481 ◽  
Author(s):  
R. M. Cohen
Keyword(s):  
Phase Diagram ◽  
Experimental Design ◽  
Equilibrium State ◽  
Tracer Diffusion ◽  
Impurity Diffusion ◽  
Experimental Designs ◽  
Quasi Equilibrium ◽  
Native Defect ◽  
Phase Rule ◽  
Thermodynamic Variables

ABSTRACTIt is often incorrectly assumed that temperature alone defines the equilibrium state of a crystal. However, the Gibbs phase rule shows that the number of independent thermodynamic variables required to define the equilibrium state depends upon the experimental design. In most practical cases, this means that temperature and components of the external phase or phases in proximate contact with the sample will determine the equilibrium state, e.g., the equilibrium native defect concentrations, impurity solubility, etc. If native defect concentrations approach their equilibrium values in a time which is short compared to the time of an experiment, then impurity diffusion can be described well by a thermodynamic model and impurity diffusion is analogous to classic tracer diffusion. If native defect concentrations require a long time to approach their equilibrium values, then diffusivities will exhibit significant time dependence and simple models do not apply. However, multi-phase, multi-component systems generally have several possible equilibrium regions within their phase diagram. Relating the phase diagram to a given experimental design allows one to qualitatively understand how the native defect concentrations change as a crystal in a nonequilibrium state relaxes toward one (of several possible) well-defined equilibrium states. Examples will focus largely on the diffusion of impurities in single crystal GaAs. Evidence will be presented that native defect concentrations can rapidly approach equilibrium in a limited group of experimental designs. We shall show why a description of diffusivity in terms of carrier concentration, a dependent thermodynamic variable, sometimes succeeds but often fails. Examples of commonly used experimental designs, in which there is inadequate control over the independent variables, will demonstrate some large variations in measured diffusivity. An enormous range of reported diffusivities, in GaAs covered by SiO2 or Si3N4 encapsulant layers, will demonstrate the difficulty and the futility of measuring diffusion when the solid is cut off from the external phases which define the equilibrium state.

scholarly journals Break-away separation for high turbulence intensity and large Reynolds number

2011 ◽  
Vol 670 ◽  
pp. 260-300 ◽  
Author(s):  
B. SCHEICHL ◽  
A. KLUWICK ◽  
F. T. SMITH
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulence Intensity ◽  
Rapid Change ◽  
Separation Process ◽  
Large Reynolds Number ◽  
Self Consistent ◽  
High Turbulence ◽  
Experimental Findings ◽  
Theoretical Results

Massive flow separation from the surface of a plane bluff obstacle in an incompressible uniform stream is addressed theoretically for large values of the global Reynolds numberRe. The analysis is motivated by a conclusion drawn from recent theoretical results which is corroborated by experimental findings but apparently contrasts with common reasoning: the attached boundary layer extending from the front stagnation point to the position of separation never attains a fully developed turbulent state, even for arbitrarily largeRe. Consequently, the boundary layer exhibits a certain level of turbulence intensity that is linked with the separation process, governed by local viscous–inviscid interaction. Eventually, the latter mechanism is expected to be associated with rapid change of the separating shear layer towards a fully developed turbulent one. A self-consistent flow description in the vicinity of separation is derived, where the present study includes the predominantly turbulent region. We establish a criterion that acts to select the position of separation. The basic analysis here, which appears physically feasible and rational, is carried out without needing to resort to a specific turbulence closure.

scholarly journals Gravity analog model of non-equilibrium thermodynamics

2019 ◽  
Vol 2019 (7) ◽  
Author(s):  
Noriaki Aibara ◽  
Naoaki Fujimoto ◽  
So Katagiri ◽  
Mayumi Saitou ◽  
Akio Sugamoto ◽  
...  
Keyword(s):  
Time Reversal ◽  
Resonance Problem ◽  
Quasi Equilibrium ◽  
Closed Path ◽  
Equilibrium Thermodynamics ◽  
Analog Model ◽  
Metric Tensor ◽  
Kinetic Coefficients ◽  
Thermodynamic Variables ◽  
Non Equilibrium

Abstract The non-equilibrium thermodynamics of Onsager and Machlup and of Hashitsume is reformulated as a gravity analog model, in which thermodynamic variables, kinetic coefficients, and generalized forces form, respectively, coordinates and metric tensor and vector fields in a space of thermodynamic variables. The relevant symmetry of the model is the general coordinate transformation. Then, the entropy production is classified into three categories, when a closed path is depicted as a thermodynamic cycle. One category is time-reversal odd, and is attributed to the number of lines of magnetic flux passing through the closed path, having the monopole as a source. There are two time-reversal-even categories, one of which is attributed to the space curvature around the path, having the gravitational instanton as a source, which dominates for a rapid operation of the cycle. The last category is the usual one, which remains even for the quasi-equilibrium operation. It is possible to extend the model to include non-linear responses. In introducing new terms, dimensional counting is important, using two parameters, the temperature and the relaxation time. The effective action, being induced by the non-equilibrium thermodynamics, is derived. This is a candidate for the action that controls the dynamics of kinetic coefficients and thermodynamic forces. An example is given in a chemical oscillatory reaction in a solvent of van der Waals type. The fluctuation–dissipation theorem is examined à la Onsager, and a derivation of the gravity analog thermodynamic model from quantum mechanics is sketched, based on an analogy to the resonance problem.

IDEAL TURBULENCE IN AN IDEALIZED TIME-DELAYED CHUA’S CIRCUIT

1994 ◽  
Vol 04 (02) ◽  
pp. 303-309 ◽  
Author(s):  
A.N. SHARKOVSKY
Keyword(s):  
Differential Equations ◽  
Short Circuit ◽  
Nonlinear Difference Equation ◽  
Weak Turbulence ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Random Functions ◽  
Strong Turbulence ◽  
Linear Partial Differential Equations ◽  
Lc Resonator

By replacing the parallel LC “resonator” in Chua’s circuit by a lossless transmission line, terminated by a short circuit, we obtain a “time-delayed Chua’s circuit” whose time evolution is described by a pair of linear partial differential equations with a nonlinear boundary condition. If we neglect the capacitance across the Chua’s diode, described by a nonsymmetric piecewiselinear vR–iR characteristic, the resulting idealized time-delayed Chua’s circuit is described exactly by a scalar nonlinear difference equation with continuous time, which makes it possible to characterize its associated nonlinear dynamics and spatial chaotic phenomena. From a mathematical viewpoint, circuits described by ordinary differential equations can generate only temporal chaos, while the time-delayed Chua’s circuit can generate spatiotem poral chaos. Except for stepwise periodic oscillations, the typical solutions of the idealized time-delayed Chua’s circuit consist of either weak turbulence, or strong turbulence, which are examples of “ideal” (or “dry”) turbulence. In both cases, we can observe infinite processes of spatiotemporal coherent structure formations. Under weak turbulence, the graphs of the solution tend to limit sets which are fractals with a Hausdorff dimension between 1 and 3, and is therefore larger than the topological dimension (of sets). Under strong turbulence, the “limit” oscillations are oscillations whose amplitudes are random functions. This means that the attractor of the idealized time-delayed Chua’s circuit already contains random functions, and spatial self-stochasticity phenomenon can be observed.

Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

1998 ◽  
Vol 37 (03) ◽  
pp. 235-238 ◽  
Author(s):  
M. El-Taha ◽  
D. E. Clark
Keyword(s):  
Monte Carlo ◽  
Decision Trees ◽  
Computer Algebra ◽  
Taylor Series ◽  
Computer Algebra System ◽  
Random Variable ◽  
Monte Carlo Analysis ◽  
Normal Random Variable ◽  
Medical Decision ◽  
Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

Investigating the Nonlinear Optical Response of Pepper Oil under Low Power Irradiation with Continuous Wave Visible Laser Beam

2020 ◽  
pp. 131-138
Keyword(s):  
Refractive Index ◽  
Nonlinear Refractive Index ◽  
Nonlinear Optical ◽  
Continuous Wave ◽  
Diffraction Integral ◽  
Visible Laser ◽  
Limiting Property ◽  
Kirchhoff Diffraction Integral ◽  
Theoretical Results ◽  
Good Agreement

The nonlinear optical properties of pepper oil are studied by diffraction ring patterns and Z-scan techniques with continuous wave beam from solid state laser at 473 nm wavelength. The nonlinear refractive index of the sample is calculated by both techniques. The sample show high nonlinear refractive index. Based on Fresnel-Kirchhoff diffraction integral, the far-field intensity distributions of ring patterns have been calculated. It is found that the experimental results are in good agreement with the theoretical results. Also the optical limiting property of pepper oil is reported. The results obtained in this study prove that the pepper oil has applications in nonlinear optical devices.

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