Effect of Heat Transfer on Pipe Flow Stability

2017 ◽  
Author(s):  
Ce Zhang ◽  
Wei Ma ◽  
Wensheng Yu ◽  
Jinfang Teng
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Flow Field ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Pipe Flow ◽  
Cfd Simulation ◽  
Stokes Equations ◽  
Flow Stability ◽  
Global Mode

The compressibility of flow field has an important effect on flow stability. However, when the compressibility is considered, the effect of Mach number is often considered while the effect of heat transfer is always neglected in the existing flow stability studies. Linear stability analysis tools based on compressible Orr-Sommerfeld (O-S) equations and linearized Navier-Stokes equations in cylindrical coordinate system are established in this paper. These equations are numerically solved by using Chebyshev spectral collocation method and pseudo-modes are eliminated. Linear stability analysis of pipe flow with heat transfer whose average flow field is obtained by CFD simulation is carried out. The results show that for spatial modes, the heating effect of the wall makes pipe flow more unstable, while cooling effect of the wall makes pipe flow more stable. For global modes of pipe flow, the frequency of global mode decreases when the wall cools the flow and the decrease of mean temperature of pipe flow leads to the improvement of global mode stability.

Variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells. Part 1. Linear stability analysis

2013 ◽  
Vol 721 ◽  
pp. 268-294 ◽  
Author(s):  
L. Talon ◽  
N. Goyal ◽  
E. Meiburg
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Stokes Equations ◽  
Variable Density ◽  
Local Concentration ◽  
Miscible Displacements ◽  
Instability Modes ◽  
Finger Tip

AbstractA computational investigation of variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells is presented. As a first step, two-dimensional base states are obtained by means of simulations of the Stokes equations, which are nonlinear due to the dependence of the viscosity on the local concentration. Here, the vertical position of the displacement front is seen to reach a quasisteady equilibrium value, reflecting a balance between viscous and gravitational forces. These base states allow for two instability modes: first, there is the familiar tip instability driven by the unfavourable viscosity contrast of the displacement, which is modulated by the presence of density variations in the gravitational field; second, a gravitational instability occurs at the unstably stratified horizontal interface along the side of the finger. Both of these instability modes are investigated by means of a linear stability analysis. The gravitational mode along the side of the finger is characterized by a wavelength of about one half to one full gap width. It becomes more unstable as the gravity parameter increases, even though the interface is shifted closer to the wall. The growth rate is largest far behind the finger tip, where the interface is both thicker, and located closer to the wall, than near the finger tip. The competing influences of interface thickness and wall proximity are clarified by means of a parametric stability analysis. The tip instability mode represents a gravity-modulated version of the neutrally buoyant mode. The analysis shows that in the presence of density stratification its growth rate increases, while the dominant wavelength decreases. This overall destabilizing effect of gravity is due to the additional terms appearing in the stability equations, which outweigh the stabilizing effects of gravity onto the base state.

Linear Stability Analysis and Application of a New Solution Method of the Elastodynamic Equations Suitable for a Unified Fluid-Structure-Interaction Approach

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
C. G. Giannopapa ◽  
G. Papadakis
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Solution Method ◽  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Analytic Solutions ◽  
Computational Domain ◽  
Fluid Structure ◽  
Structure Interaction

In the conventional approach for fluid-structure-interaction problems, the fluid and solid components are treated separately and information is exchanged across their interface. According to the conventional terminology, the current numerical methods can be grouped in two major categories: partitioned methods and monolithic methods. Both methods use separate sets of equations for fluid and solid that have different unknown variables. A unified solution method has been presented in the previous work of Giannopapa and Papadakis (2004, “A New Formulation for Solids Suitable for a Unified Solution Method for Fluid-Structure Interaction Problems,” ASME PVP 2004, San Diego, CA, July, PVP Vol. 491–1, pp. 111–117), which is different from these methods. The new approach treats both fluid and solid as a single continuum; thus, the whole computational domain is treated as one entity discretized on a single grid. Its behavior is described by a single set of equations, which are solved fully implicitly. In this paper, the elastodynamic equations are reformulated so that they contain the same unknowns as the Navier–Stokes equations, namely, velocities and pressure. Two time marching and one spatial discretization scheme, widely used for fluid equations, are applied for the solution of the reformulated equations for solids. Using linear stability analysis, the accuracy and dissipation characteristics of the resulting difference equations are examined. The aforementioned schemes are applied to a transient structural problem (beam bending) and the results compare favorably with available analytic solutions and are consistent with the conclusions of the stability analysis. A parametric investigation using different meshes, time steps, and beam dimensions is also presented. For all cases examined, the numerical solution was stable and robust and therefore is suitable for the next stage of application to full fluid-structure-interaction problems.

scholarly journals Deep-water sediment wave formation: linear stability analysis of coupled flow/bed interaction

2011 ◽  
Vol 680 ◽  
pp. 435-458 ◽  
Author(s):  
L. LESSHAFFT ◽  
B. HALL ◽  
E. MEIBURG ◽  
B. KNELLER
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Internal Wave ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Stokes Equations ◽  
Wave Mode ◽  
Bottom Current ◽  
Field Observations ◽  
Sediment Bed

A linear stability analysis is carried out for the interaction of an erodible sediment bed with a sediment-laden, stratified flow above the bed, such as a turbidity or bottom current. The fluid motion is described by the full, two-dimensional Navier–Stokes equations in the Boussinesq approximation, while erosion is modelled as a diffusive flux of particles from the bed into the fluid. The stability analysis shows the existence of both Tollmien–Schlichting and internal wave modes in the stratified boundary layer. For the internal wave mode, the stratified boundary layer acts as a wave duct, whose height can be determined analytically from the Brunt–Väisälä frequency criterion. Consistent with this criterion, distinct unstable perturbation wavenumber regimes exist for the internal wave mode, which are associated with different numbers of pressure extrema in the wall-normal direction. For representative turbidity current parameters, the analysis predicts unstable wavelengths that are consistent with field observations. As a key condition for instability to occur, the base flow velocity boundary layer needs to be thinner than the corresponding concentration boundary layer. For most of the unstable wavenumber ranges, the phase relations between the sediment bed deformation and the associated wall shear stress and concentration perturbations are such that the sediment waves migrate in the upstream direction, which again is consistent with field observations.

Shear-flow stability within the atmosphere of Venus

1974 ◽  
Vol 66 (2) ◽  
pp. 267-272 ◽  
Author(s):  
R. D. Cess ◽  
Harshvardhan
Keyword(s):  
Stability Analysis ◽  
Radiative Transfer ◽  
Shear Flow ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Flow Instability ◽  
Flow Stability ◽  
Shear Flow Instability ◽  
Realistic Formulation ◽  
Atmosphere Of Venus

Employing a linear stability analysis, Dudis (1973) has recently suggested that shear-flow instability might exist within the upper stratosphere of Venus owing to destabilization by radiative transfer. We have incorporated a more realistic formulation for radiative transfer into his stability analysis and conclude that such an instability is unlikely.

scholarly journals The impact of heating the breakdown bubble on the global mode of a swirling jet: Experiments and linear stability analysis

2016 ◽  
Vol 28 (10) ◽  
pp. 104102 ◽  
Author(s):  
Lothar Rukes ◽  
Moritz Sieber ◽  
C. Oliver Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Global Mode ◽  
Swirling Jet ◽  
The Impact

Variable-density miscible displacements in a vertical Hele-Shaw cell: linear stability

2007 ◽  
Vol 584 ◽  
pp. 357-372 ◽  
Author(s):  
N. GOYAL ◽  
H. PICHLER ◽  
E. MEIBURG
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Stokes Equations ◽  
Capillary Tube ◽  
Computational Study ◽  
Stability Limit ◽  
Dominant Wavelength ◽  
Miscible Displacements

A computational study based on the Stokes equations is conducted to investigate the effects of gravitational forces on miscible displacements in vertical Hele-Shaw cells. Nonlinear simulations provide the quasi-steady displacement fronts in the gap of the cell, whose stability to spanwise perturbations is subsequently examined by means of a linear stability analysis. The two-dimensional simulations indicate a marked thickening (thinning) and slowing down (speeding up) of the displacement front for flows stabilized (destabilized) by gravity. For the range investigated, the tip velocity is found to vary linearly with the gravity parameter. Strongly stable density stratifications lead to the emergence of flow patterns with spreading fronts, and to the emergence of a secondary needle-shaped finger, similar to earlier observations for capillary tube flows. In order to investigate the transition between viscously driven and purely gravitational instabilities, a comparison is presented between displacement flows and gravity-driven flows without net displacements.The linear stability analysis shows that both the growth rate and the dominant wavenumber depend only weakly on the Péclet number. The growth rate varies strongly with the gravity parameter, so that even a moderately stable density stratification can stabilize the displacement. Both the growth rate and the dominant wavelength increase with the viscosity ratio. For unstable density stratifications, the dominant wavelength is nearly independent of the gravity parameter, while it increases strongly for stable density stratifications. Finally, the kinematic wave theory of Lajeunesse et al. (J. Fluid Mech. vol. 398, 1999, p. 299) is seen to capture the stability limit quite accurately, while the Darcy analysis misses important aspects of the instability.

scholarly journals An Improved Lattice Hydrodynamic Model by considering the Effect of “Backward-Looking” and Anticipation Behavior

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Jin Wan ◽  
Xin Huang ◽  
Wenzhi Qin ◽  
Xiuge Gu ◽  
Min Zhao
Keyword(s):  
Stability Analysis ◽  
Traffic Flow ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Hydrodynamic Model ◽  
Traffic Congestion ◽  
Traffic Accidents ◽  
Flow Stability ◽  
Lattice Hydrodynamic Model ◽  
Traffic Flow Stability

In order to prevent the occurrence of traffic accidents, drivers always focus on the running conditions of the preceding and rear vehicles to change their driving behavior. By taking into the “backward-looking” effect and the driver’s anticipation effect of flux difference consideration at the same time, a novel two-lane lattice hydrodynamic model is proposed to reveal driving characteristics. The corresponding stability conditions are derived through a linear stability analysis. Then, the nonlinear theory is also applied to derive the mKdV equation describing traffic congestion near the critical point. Linear and nonlinear analyses of the proposed model show that how the “backward-looking” effect and the driver’s anticipation behavior comprehensively affect the traffic flow stability. The results show that the positive constant γ , the driver’s anticipation time τ , and the sensitivity coefficient p play significant roles in the improvement of traffic flow stability and the alleviation of the traffic congestion. Furthermore, the effectiveness of linear stability analysis and nonlinear analysis results is demonstrated by numerical simulations.

Impact of Flow Non-Axisymmetry on Swirling Flow Dynamics and Receptivity to Acoustics

2015 ◽  
Author(s):  
Samuel Hansford ◽  
Jacqueline O’Connor ◽  
Kiran Manoharan ◽  
Santosh Hemchandra
Keyword(s):  
Stability Analysis ◽  
Velocity Field ◽  
Flow Field ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Swirling Flow ◽  
Forced Response ◽  
Experimental Results ◽  
Transverse Acoustic ◽  
Jet Axis

In this study, we experimentally investigate both the intrinsic instability characteristics and forced response to transverse acoustic excitation of a non-reacting, swirling flow for application to combustion instability in annular gas turbine engines. The non-axisymmetry of the velocity field is quantified using an azimuthal mode decomposition of the time-averaged velocity field that shows that (1) the flow field is largely axisymmetric, (2) axisymmetry decreases with downstream distance, and (3) forcing does not significantly alter the time-averaged shape of the flow field. The flow field is analyzed in a companion linear stability analysis that shows that the most unstable modes in the flow field are m=−1 and m=−2, which agrees with the experimental observations and shows that the intrinsic dynamics of this flow field are non-axisymmetric with respect to the jet axis. The linear stability analysis captures the spatial variation of mode strength for certain modes, particularly mode m=−1, but there are some deviations from the experimental results. Most notably, these deviations occur for mode m=0 at radii away from the jet axis. Experimental results of the forced response of the flow indicate that the intrinsic instability characteristics of the flow field have an impact on the forced-response dynamics. Response of the flow field to a velocity anti-node in a standing transverse acoustic field shows non-axisymmetric vortex rollup and the dominance of the m=−1 and m=1 azimuthal modes in the fluctuating flow field. In the presence of a pressure anti-node, the m=0 mode of the fluctuating flow field is very strong at the jet exit, indicating an axisymmetric response, and ring vortex shedding is apparent in the flow measurements from high-speed PIV. However, further downstream, the strength of the axisymmetric mode decreases and the m=−1 and m=1 modes dominate, resulting in a tilting of the vortex ring as it convects downstream. Implications for flame response to transverse acoustic fields are discussed.

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