scholarly journals Response of a swirl flame to inertial waves

2017 ◽  
Vol 10 (4) ◽  
pp. 277-286 ◽  
Author(s):  
Alp Albayrak ◽  
Deniz A Bezgin ◽  
Wolfgang Polifke
Keyword(s):  
Steady State ◽  
Impulse Response ◽  
Finite Impulse Response ◽  
Reactive Flow ◽  
Inertial Waves ◽  
Mean Flow ◽  
Flow Equations ◽  
Flame Response ◽  
Inertial Wave ◽  
The Impact

Acoustic waves passing through a swirler generate inertial waves in rotating flow. In the present study, the response of a premixed flame to an inertial wave is scrutinized, with emphasis on the fundamental fluid-dynamic and flame-kinematic interaction mechanism. The analysis relies on linearized reactive flow equations, with a two-part solution strategy implemented in a finite element framework: Firstly, the steady state, low-Mach number, Navier–Stokes equations with Arrhenius type one-step reaction mechanism are solved by Newton’s method. The flame impulse response is then computed by transient solution of the analytically linearized reactive flow equations in the time domain, with mean flow quantities provided by the steady-state solution. The corresponding flame transfer function is retrieved by fitting a finite impulse response model. This approach is validated against experiments for a perfectly premixed, lean, methane-air Bunsen flame, and then applied to a laminar swirling flame. This academic case serves to investigate in a generic manner the impact of an inertial wave on the flame response. The structure of the inertial wave is characterized by modal decomposition. It is shown that axial and radial velocity fluctuations related to the eigenmodes of the inertial wave dominate the flame front modulations. The dispersive nature of the eigenmodes plays an important role in the flame response.

scholarly journals Global Systems for Mobile Position Tracking Using Kalman and Lainiotis Filters

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Nicholas Assimakis ◽  
Maria Adam
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Impulse Response ◽  
Finite Impulse Response ◽  
Position Tracking ◽  
Computational Burden ◽  
Time Invariant ◽  
Global Systems

We present two time invariant models for Global Systems for Mobile (GSM) position tracking, which describe the movement inx-axis andy-axis simultaneously or separately. We present the time invariant filters as well as the steady state filters: the classical Kalman filter and Lainiotis Filter and the Join Kalman Lainiotis Filter, which consists of the parallel usage of the two classical filters. Various implementations are proposed and compared with respect to their behavior and to their computational burden: all time invariant and steady state filters have the same behavior using both proposed models but have different computational burden. Finally, we propose a Finite Impulse Response (FIR) implementation of the Steady State Kalman, and Lainiotis filters, which does not require previous estimations but requires a well-defined set of previous measurements.

Quantification of the Impact of Uncertainties in Operating Conditions on the Flame Transfer Function With Non-Intrusive Polynomial Chaos Expansion

2018 ◽  
Author(s):  
Alexander Avdonin ◽  
Wolfgang Polifke
Keyword(s):  
Transfer Function ◽  
Impulse Response ◽  
Equivalence Ratio ◽  
Polynomial Chaos ◽  
Finite Impulse Response ◽  
Operating Parameter ◽  
Polynomial Chaos Expansion ◽  
Operating Conditions ◽  
Chaos Expansion ◽  
The Impact

Non-intrusive polynomial chaos expansion (NIPCE) is used to quantify the impact of uncertainties in operating conditions on the flame transfer function of a premixed laminar flame. NIPCE requires only a small number of system evaluations, so it can be applied in cases where a Monte Carlo simulation is unfeasible. We consider three uncertain operating parameters: inlet velocity, burner plate temperature, and equivalence ratio. The flame transfer function (FTF) is identified in terms of the finite impulse response from CFD simulations with broadband velocity excitation. NIPCE yields uncertainties in the FTF due to the uncertain operating conditions. For the chosen uncertain operating bounds, a second-order expansion is found to be sufficient to represent the resulting uncertainties in the FTF with good accuracy. The effect of each operating parameter on the FTF is studied using Sobol indices, i.e. a variance-based measure of sensitivity, which are computed from the NIPCE. It is observed that in the present case uncertainties in the finite impulse response as well as in the phase of the FTF are dominated by the equivalence-ratio uncertainty. For frequencies below 150 Hz, the uncertainty in the gain of the FTF is also attributable to the uncertainty in equivalence-ratio, but for higher frequencies the uncertainties in velocity and temperature dominate. At last, we adopt the polynomial approximation of the output quantity, provided by the NIPCE method, for further UQ studies with modified input uncertainties.

Quantification and Propagation of Uncertainties in Identification of Flame Impulse Response for Thermoacoustic Stability Analysis

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Shuai Guo ◽  
Camilo F. Silva ◽  
Abdulla Ghani ◽  
Wolfgang Polifke
Keyword(s):  
Growth Rate ◽  
Time Series ◽  
Stability Analysis ◽  
Impulse Response ◽  
Cfd Simulation ◽  
Finite Impulse Response ◽  
Original System ◽  
Dimensional Approximation ◽  
Fir Model ◽  
The Impact

The thermoacoustic behavior of a combustion system can be determined numerically via acoustic tools such as Helmholtz solvers or network models coupled with a model for the flame dynamic response. Within such a framework, the flame response to flow perturbations can be described by a finite impulse response (FIR) model, which can be derived from large eddy simulation (LES) time series via system identification. However, the estimated FIR model will inevitably contain uncertainties due to, e.g., the statistical nature of the identification process, low signal-to-noise ratio, or finite length of time series. Thus, a necessary step toward reliable thermoacoustic stability analysis is to quantify the impact of uncertainties in FIR model on the growth rate of thermoacoustic modes. There are two practical considerations involved in this topic. First, how to efficiently propagate uncertainties from the FIR model to the modal growth rate of the system, considering it is a high dimensional uncertainty quantification (UQ) problem? Second, since longer computational fluid dynamics (CFD) simulation time generally leads to less uncertain FIR model identification, how to determine the length of the CFD simulation required to obtain satisfactory confidence? To address the two issues, a dimensional reduction UQ methodology called “Active subspace approach (ASA)” is employed in the present study. For the first question, ASA is applied to exploit a low-dimensional approximation of the original system, which allows accelerated UQ analysis. Good agreement with Monte Carlo analysis demonstrates the accuracy of the method. For the second question, a procedure based on ASA is proposed, which can serve as an indicator for terminating CFD simulation. The effectiveness of the procedure is verified in the paper.

Quantification and Propagation of Uncertainties in Identification of Flame Impulse Response for Thermoacoustic Stability Analysis

2018 ◽  
Author(s):  
Shuai Guo ◽  
Camilo F. Silva ◽  
Abdulla Ghani ◽  
Wolfgang Polifke
Keyword(s):  
Growth Rate ◽  
Time Series ◽  
Stability Analysis ◽  
Impulse Response ◽  
Cfd Simulation ◽  
Finite Impulse Response ◽  
Dimensional Approximation ◽  
Fir Model ◽  
The Impact ◽  
Active Subspace

The thermoacoustic behavior of a combustion system can be determined numerically via acoustic tools such as Helmholtz solvers or network models coupled with a model for the flame dynamic response. Within such a framework, the flame response to flow perturbations can be described by a Finite Impulse Response (FIR) model, which can be derived from LES time series via system identification. However, the estimated FIR model will inevitably contain uncertainties due to e.g., the statistical nature of the identification process, low signal-to-noise ratio or finite length of time series. Thus, a necessary step towards reliable thermoacoustic stability analysis is to quantify the impact of uncertainties in FIR model on the growth rate of thermoacoustic modes. There are two practical considerations involved in this topic. First, how to efficiently propagate uncertainties from the FIR model to the modal growth rate of the system, considering it is a high dimensional uncertainty quantification (UQ) problem? Second, since longer CFD simulation time generally leads to less uncertain FIR model identification, how to determine the length of the CFD simulation required to obtain satisfactory confidence? To address the two issues, a dimensional reduction UQ methodology called “Active Subspace approach” is employed in the present study. For the first question, Active Subspace approach is applied to exploit a low-dimensional approximation of the original system, which allows accelerated UQ analysis. Good agreement with Monte Carlo analysis demonstrates the accuracy of the method. For the second question, a procedure based on Active Subspace approach is proposed, which can serve as an indicator for terminating CFD simulation. The effectiveness of the procedure is verified in the paper.

scholarly journals Distributed Periodic Steady State Kalman Filter

2022 ◽  
Vol 16 ◽  
pp. 668-674
Author(s):  
Nicholas Assimakis ◽  
Maria Adam ◽  
Christos Massouros
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Impulse Response ◽  
Distributed Algorithm ◽  
Finite Impulse Response ◽  
Idle Time ◽  
Parallel Structure ◽  
Distributed Implementation ◽  
Periodic Steady State

In this paper a distributed implementation for the periodic steady state Kalman filter is proposed. The distributed algorithm has parallel structure and can be implemented using processors in parallel without idle time. The number of processors is equal to the model period. The resulting speedup is also derived. The Finite Impulse Response (FIR) form of the periodic steady state Kalman filter is derived.

The formulation of the RANS equations for supersonic and hypersonic turbulent flows

2020 ◽  
pp. 1-31
Author(s):  
H. Zhang ◽  
T.J. Craft ◽  
H. Iacovides
Keyword(s):  
Kinetic Energy ◽  
Pressure Gradient ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
High Speed ◽  
Mean Flow ◽  
Rans Equations ◽  
Flow Equations ◽  
The Mean ◽  
The Impact

Abstract Accurate prediction of supersonic and hypersonic turbulent flows is essential to the design of high-speed aerospace vehicles. Such flows are mainly predicted using the Reynolds-Averaged Navier–Stokes (RANS) approach in general, and in particular turbulence models using the effective viscosity approximation. Several terms involving the turbulent kinetic energy (k) appear explicitly in the RANS equations through the modelling of the Reynolds stresses in such approach, and similar terms appear in the mean total energy equation. Some of these terms are often ignored in low, or even supersonic, speed simulations with zero-equation models, as well as some one- or two-equation models. The omission of these terms may not be appropriate under hypersonic conditions. Nevertheless, this is a widespread practice, even for very high-speed turbulent flow simulations, because many software packages still make such approximations. To quantify the impact of ignoring these terms in the RANS equations, two linear two-equation models and one non-linear two-equation model are applied to the computation of five supersonic and hypersonic benchmark cases, one 2D zero-pressure gradient hypersonic flat plate case and four shock wave boundary layer interaction (SWBLI) cases. The surface friction coefficients and velocity profiles predicted with different combinations of the turbulent kinetic energy terms present in the transport equations show little sensitivity to the presence of these terms in the zero-pressure gradient case. In the SWBLI cases, however, comparisons show that inclusion of k in the mean flow equations can have a strong effect on the prediction of flow separation. Therefore, it is highly recommended to include all the turbulent kinetic energy terms in the mean flow equations when dealing with simulations of supersonic and hypersonic turbulent flows, especially for flows with SWBLIs. As a further consequence, since k may not be obtained explicitly in zero-equation, or certain one-equation, models, it is debatable whether these models are suitable for simulations of supersonic and hypersonic turbulent flows with SWBLIs.

The energetics of the interaction between short small-amplitude internal waves and inertial waves

1988 ◽  
Vol 196 ◽  
pp. 93-106 ◽  
Author(s):  
D. Broutman ◽  
R. Grimshaw
Keyword(s):  
Wave Field ◽  
Internal Waves ◽  
Small Amplitude ◽  
Short Wave ◽  
Finite Amplitude ◽  
Inertial Waves ◽  
Mean Flow ◽  
Total Energy Balance ◽  
Inertial Wave ◽  
Wave Induced

The interaction between a wave packet of small-amplitude short internal waves, and a finite-amplitude inertial wave field is described to second order in the short-wave amplitude. The discussion is based on the principle of wave action conservation and the equations for the wave-induced Lagrangian mean flow. It is demonstrated that as the short internal waves propagate through the inertial wave field they generate a wave-induced train of trailing inertial waves. The contribution of this wave-induced mean flow to the total energy balance is described. The results obtained here complement the finding of Broutman & Young (1986) that the short internal waves undergo a net change in energy after their encounter with the inertial wave field.

scholarly journals Advanced Constitutive Modeling of the Thixotropic Elasto-Visco-Plastic Behavior of Blood: Steady-State Blood Flow in Microtubes

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 367
Author(s):  
Konstantinos Giannokostas ◽  
Yannis Dimakopoulos ◽  
Andreas Anayiotos ◽  
John Tsamopoulos
Keyword(s):  
Blood Flow ◽  
Steady State ◽  
Constitutive Model ◽  
Blood Plasma ◽  
Constitutive Modeling ◽  
Flow Direction ◽  
Momentum Balance ◽  
Plastic Behavior ◽  
Flow Investigation ◽  
The Impact

The present work focuses on the in-silico investigation of the steady-state blood flow in straight microtubes, incorporating advanced constitutive modeling for human blood and blood plasma. The blood constitutive model accounts for the interplay between thixotropy and elasto-visco-plasticity via a scalar variable that describes the level of the local blood structure at any instance. The constitutive model is enhanced by the non-Newtonian modeling of the plasma phase, which features bulk viscoelasticity. Incorporating microcirculation phenomena such as the cell-free layer (CFL) formation or the Fåhraeus and the Fåhraeus-Lindqvist effects is an indispensable part of the blood flow investigation. The coupling between them and the momentum balance is achieved through correlations based on experimental observations. Notably, we propose a new simplified form for the dependence of the apparent viscosity on the hematocrit that predicts the CFL thickness correctly. Our investigation focuses on the impact of the microtube diameter and the pressure-gradient on velocity profiles, normal and shear viscoelastic stresses, and thixotropic properties. We demonstrate the microstructural configuration of blood in steady-state conditions, revealing that blood is highly aggregated in narrow tubes, promoting a flat velocity profile. Additionally, the proper accounting of the CFL thickness shows that for narrow microtubes, the reduction of discharged hematocrit is significant, which in some cases is up to 70%. At high pressure-gradients, the plasmatic proteins in both regions are extended in the flow direction, developing large axial normal stresses, which are more significant in the core region. We also provide normal stress predictions at both the blood/plasma interface (INS) and the tube wall (WNS), which are difficult to measure experimentally. Both decrease with the tube radius; however, they exhibit significant differences in magnitude and type of variation. INS varies linearly from 4.5 to 2 Pa, while WNS exhibits an exponential decrease taking values from 50 mPa to zero.

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