scholarly journals Nonlinear sound propagation in two-dimensional curved ducts: a multimodal approach

2019 ◽  
Vol 875 ◽  
pp. 411-447
Author(s):  
James P. McTavish ◽  
Edward J. Brambley
Keyword(s):  
Sound Propagation ◽  
Complex Geometry ◽  
Radiation Condition ◽  
Two Dimensional ◽  
Multimodal Approach ◽  
General Shape ◽  
Weakly Nonlinear ◽  
Acoustic Reflection ◽  
Nonlinear Acoustic ◽  
Curved Ducts

A method for studying weakly nonlinear acoustic propagation in two-dimensional ducts of general shape – including curvature and variable width – is presented. The method is based on a local modal decomposition of the pressure and velocity in the duct. A pair of nonlinear ordinary differential equations for the modal amplitudes of the pressure and velocity modes is derived. To overcome the inherent instability of these equations, a nonlinear admittance relation between the pressure and velocity modes is presented, introducing a novel ‘nonlinear admittance’ term. Appropriate equations for the admittance are derived which are to be solved through the duct, with a radiation condition applied at the duct exit. The pressure and velocity are subsequently found by integrating an equation involving the admittance through the duct. The method is compared, both analytically and numerically, against published results and the importance of nonlinearity is demonstrated in ducts of complex geometry. Comparisons between ducts of differing geometry are also performed to illustrate the effect of geometry on nonlinear sound propagation. A new ‘nonlinear reflectance’ term is introduced, providing a more complete description of acoustic reflection that also takes into account the amplitude of the incident wave.

Comparison of DSMC and CFD Models of Heat Transfer in a Rarefied Two-Dimensional Geometry

2018 ◽  
Author(s):  
Dilesh Maharjan ◽  
Mustafa Hadj-Nacer ◽  
Miles Greiner ◽  
Stefan K. Stefanov
Keyword(s):  
Heat Transfer ◽  
Rarefied Gas ◽  
Complex Geometry ◽  
Direct Simulation Monte Carlo ◽  
Accurate Method ◽  
Vacuum Drying ◽  
Helium Pressure ◽  
Two Dimensional ◽  
Dsmc Method ◽  
Cfd Simulations

During vacuum drying of used nuclear fuel (UNF) canisters, helium pressure is reduced to as low as 67 Pa to promote evaporation and removal of remaining water after draining process. At such low pressure, and considering the dimensions of the system, helium is mildly rarefied, which induces a thermal-resistance temperature-jump at gas–solid interfaces that contributes to the increase of cladding temperature. It is important to maintain the temperature of the cladding below roughly 400 °C to avoid radial hydride formation, which may cause cladding embrittlement during transportation and long-term storage. Direct Simulation Monte Carlo (DSMC) method is an accurate method to predict heat transfer and temperature under rarefied condition. However, it is not convenient for complex geometry like a UNF canister. Computational Fluid Dynamics (CFD) simulations are more convenient to apply but their accuracy for rarefied condition are not well established. This work seeks to validate the use of CFD simulations to model heat transfer through rarefied gas in simple two-dimensional geometry by comparing the results to the more accurate DSMC method. The geometry consists of a circular fuel rod centered inside a square cross-section enclosure filled with rarefied helium. The validated CFD model will be used later to accurately estimate the temperature of an UNF canister subjected to vacuum drying condition.

Three-dimensional disturbances to a mixing layer in the nonlinear critical-layer regime

1995 ◽  
Vol 291 ◽  
pp. 57-81 ◽  
Author(s):  
S. M. Churilov ◽  
I. G. Shukhman
Keyword(s):  
Travelling Waves ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Critical Layer ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
New Type ◽  
Two Stages

We consider the nonlinear spatial evolution in the streamwise direction of slightly three-dimensional disturbances in the form of oblique travelling waves (with spanwise wavenumber kz much less than the streamwise one kx) in a mixing layer vx = u(y) at large Reynolds numbers. A study is made of the transition (with the growth of amplitude) to the regime of a nonlinear critical layer (CL) from regimes of a viscous CL and an unsteady CL, which we have investigated earlier (Churilov & Shukhman 1994). We have found a new type of transition to the nonlinear CL regime that has no analogy in the two-dimensional case, namely the transition from a stage of ‘explosive’ development. A nonlinear evolution equation is obtained which describes the development of disturbances in a regime of a quasi-steady nonlinear CL. We show that unlike the two-dimensional case there are two stages of disturbance growth after transition. In the first stage (immediately after transition) the amplitude A increases as x. Later, at the second stage, the ‘classical’ law A ∼ x2/3 is reached, which is usual for two-dimensional disturbances. It is demonstrated that with the growth of kz the region of three-dimensional behaviour is expanded, in particular the amplitude threshold of transition to the nonlinear CL regime from a stage of ‘explosive’ development rises and therefore in the ‘strongly three-dimensional’ limit kz = O(kx) such a transition cannot be realized in the framework of weakly nonlinear theory.

Flow-dependent modeling of acoustic propagation based on DG-FEM method

2021 ◽  
Author(s):  
Zichen Wang ◽  
Jian Xu ◽  
Xuefeng Zhang ◽  
Can Lu ◽  
Kangkang Jin ◽  
...  
Keyword(s):  
Sound Propagation ◽  
Transmission Loss ◽  
Acoustic Propagation ◽  
Water Area ◽  
Current Speed ◽  
Propagation Model ◽  
Propagation Loss ◽  
Two Dimensional ◽  
Underwater Sound ◽  
Ocean Environment

AbstractThis paper proposes a two-dimensional underwater sound propagation model using the Discontinuous Galerkin Finite Element Method (DG-FEM) to investigate the influence of current on sound propagation. The acoustic field is calculated by the convected wave equation with the current speed parameter. Based on the current speed data from an assimilation model, a two-dimensional coupled acoustic propagation model in the Fram Strait water area is established to observe the variability in propagation loss under different seasonal velocities in the real ocean environment. The transmission loss and signal time structure are examined. The results obtained in different source frequencies are also compared. It appears that the current velocity, time and range variation all have an effect on underwater sound propagation.

scholarly journals Directional solidification of a binary alloy into a cellular convective flow: localized morphologies

1999 ◽  
Vol 395 ◽  
pp. 253-270 ◽  
Author(s):  
Y.-J. CHEN ◽  
S. H. DAVIS
Keyword(s):  
Directional Solidification ◽  
Binary Alloy ◽  
Temporal Dynamics ◽  
Three Dimensional ◽  
Multiple Scale ◽  
Solute Diffusion ◽  
Two Dimensional ◽  
Morphological Instability ◽  
Flow Strength ◽  
Weakly Nonlinear

A steady, two-dimensional cellular convection modifies the morphological instability of a binary alloy that undergoes directional solidification. When the convection wavelength is far longer than that of the morphological cells, the behaviour of the moving front is described by a slow, spatial–temporal dynamics obtained through a multiple-scale analysis. The resulting system has a parametric-excitation structure in space, with complex parameters characterizing the interactions between flow, solute diffusion, and rejection. The convection in general stabilizes two-dimensional disturbances, but destabilizes three-dimensional disturbances. When the flow is weak, the morphological instability is incommensurate with the flow wavelength, but as the flow gets stronger, the instability becomes quantized and forced to fit into the flow box. At large flow strength the instability is localized, confined in narrow envelopes. In this case the solutions are discrete eigenstates in an unbounded space. Their stability boundaries and asymptotics are obtained by a WKB analysis. The weakly nonlinear interaction is delivered through the Lyapunov–Schmidt method.

Design and Deformation of CAD Surface Models With Haptics

2004 ◽  
Author(s):  
X. Liu ◽  
G. Dodds ◽  
J. McCartney ◽  
B. K. Hinds
Keyword(s):  
Shape Control ◽  
Force Feedback ◽  
Complex Geometry ◽  
Virtual Space ◽  
Cad Model ◽  
Two Dimensional ◽  
Shape Functions ◽  
Ship Hulls ◽  
Control Functions ◽  
Surface Models

With traditional two-dimensional based interfaces, many CAD surface models, such as automobile bodies and ship hulls, are difficult to design and edit due to their 3D nature. This paper discusses the haptic-based deformation for the design of CAD surface models. With haptic devices (force feedback interfaces) designers can, in virtual space, touch a native B-rep CAD model, and use their tactile senses to manipulate it by pushing, pulling and dragging its surfaces in a natural 3D environment. The paper presents shape control functions. By using the shape functions, designers can directly manipulate and deform a selected region of a surface to the desired shape, and generate complex geometry with simple operations. Force feedback gives designers the greatest flexibility for the design of complex surfaces.

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