Numerical Study on the Effect of a Volute on Surge Phenomena in a Centrifugal Compressor

2016 ◽  
Author(s):  
S. H. Jeon ◽  
D. H. Hwang ◽  
J. H. Park ◽  
C. H. Kim ◽  
J. H. Baek ◽  
...  
Keyword(s):  
Centrifugal Compressor ◽  
Stokes Equations ◽  
Flow Instability ◽  
Numerical Study ◽  
Pressure Ratio ◽  
Unstable Flow ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Blade Passing Frequency

Numerical investigation of the effect of the volute on stall flow phenomenon is presented by solving three-dimensional Reynolds-averaged compressible Navier-Stokes equations. Two different configurations of a centrifugal compressor were used to compare their performance: One is an original centrifugal compressor which is composed of impeller, splitter, vaned diffuser and a volute and the other is the one without a volute. Steady calculations were performed to predict aerodynamic performance in terms of the pressure ratio, efficiency and mass flow rate. The results show that the operating range of the compressor with a volute is narrower than that of the compressor without a volute. This can be interpreted that flow instability is strongly influenced by the tongue of a volute which is highly asymmetric. Unsteady calculations were also performed with a time-step size of 38μs corresponding to a pitch angle of 5 degrees at the given rotational speed. The flow characteristics for two configurations are analyzed and compared at various instantaneous times showing unsteady dynamic features. Based on the unsteady flow simulation, fast Fourier transform at several discrete points in semi-vaneless space was performed at peak efficiency and near surge point in order to illustrate the unstable flow physics in both configurations. It is found that the blade passing frequency is dominant, indicating that diffuser passages have a periodicity of 40 degrees due to the rotational blades. Besides blade passing frequency, there were several noticeable frequencies which affect the instability of the whole system. Those frequencies in both configurations are compared and analyzed in various aspects.

scholarly journals Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Micropolar Fluid ◽  
Stokes Equations ◽  
Fluid Model ◽  
Navier Stokes ◽  
Optimal Order ◽  
Step Size ◽  
Time Step ◽  
Order Error ◽  
Time Step Size ◽  
Time Stepping

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.

scholarly journals Studying Inertia Effects in Open Channel Flow Using Saint-Venant Equations

Water ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 1652
Author(s):  
Dong-Sin Shih ◽  
Gour-Tsyh Yeh
Keyword(s):  
Stokes Equations ◽  
Field Application ◽  
Benchmark Problems ◽  
Algebraic Equations ◽  
Step Size ◽  
Time Step ◽  
Cross Sectional ◽  
Inertia Effects ◽  
Time Step Size ◽  
Saint Venant Equations

One-dimensional (1D) Saint-Venant equations, which originated from the Navier–Stokes equations, are usually applied to express the transient stream flow. The governing equation is based on the mass continuity and momentum equivalence. Its momentum equation, partially comprising the inertia, pressure, gravity, and friction-induced momentum loss terms, can be expressed as kinematic wave (KIW), diffusion wave (DIW), and fully dynamic wave (DYW) flow. In this study, the method of characteristics (MOCs) is used for solving the diagonalized Saint-Venant equations. A computer model, CAMP1DF, including KIW, DIW, and DYW approximations, is developed. Benchmark problems from MacDonald et al. (1997) are examined to study the accuracy of the CAMP1DF model. The simulations revealed that CAMP1DF can simulate almost identical results that are valid for various fluvial conditions. The proposed scheme that not only allows a large time step size but also solves half of the simultaneous algebraic equations. Simulations of accuracy and efficiency are both improved. Based on the physical relevance, the simulations clearly showed that the DYW approximation has the best performance, whereas the KIW approximation results in the largest errors. Moreover, the field non-prismatic case of the Zhuoshui River in central Taiwan is studied. The simulations indicate that the DYW approach does not ensure achievement of a better simulation result than the other two approximations. The investigated cross-sectional geometries play an important role in stream routing. Because of the consideration of the acceleration terms, the simulated hydrograph of a DYW reveals more physical characteristics, particularly regarding the raising and recession of limbs. Note that the KIW does not require assignment of a downstream boundary condition, making it more convenient for field application.

Analysis of the Sources and the Modal Content of the Acoustic Field in a Radial Compressor Outflow

2016 ◽  
Author(s):  
Marius C. Banica ◽  
Peter Limacher ◽  
Heinz-Jürgen Feld
Keyword(s):  
Experimental Data ◽  
Pressure Ratio ◽  
Single Point ◽  
Dipole Source ◽  
Grid Refinement ◽  
Step Size ◽  
Time Step ◽  
Vaned Diffuser ◽  
Radial Compressor ◽  
Time Step Size

In large modern turbochargers, compressors often constitute the main source of noise, with a frequency spectrum typically dominated by tonal noise at the blade passing frequency (BPF) and its harmonics. In transonic operation, inflow BPF noise is mainly generated by rotor locked shock fronts. These and the resulting acoustic fields can be predicted numerically with reasonable accuracy. Outflow noise, while also dominated by BPF tones, is linked to more complex source mechanisms. Its modal structure and the relationships between sources and modal sound pressure levels (SPL) are less well understood. Perhaps this is linked to the intrinsically non-axisymmetric geometries, which results in the need for full stage simulations if high accuracy is of paramount importance. In order to shed some light on outflow noise generation, a transient simulation of a 360° model of a radial compressor stage, including a vaned diffuser and a volute, was carried out using state-of-the-art CFD. Additionally, experimental data was gathered at a multitude of data points downstream of the volute exit for post processing and modal analysis. The sources and the propagation were calculated directly. Optimized values for tempo-spatial acoustic wave resolution and buffer layer design were chosen, based on extensive studies on simplified models. Two grid refinement levels were used to check grid convergence and time step size independence of the results was ensured. Numerical and experimental data match within 1% for total pressure ratio, volume flow and exit total temperature for the studied operating point. Both show the same modal content at the 1st BPF and indicate the presence of the same single dominating mode. The numerical results underpredict overall sound power levels (PWL) at the 1st BPF by 6.6dB. This difference is expected to decrease with further grid refinement and improved accounting for numerical damping. At the 2nd BPF, the experimental data show a significant broadening of the modal content with homogeneous modal PWL distributions. The multitude of modes leads to the generation of complex interference patterns, which shows that single-point acoustic measurements are often inadequate for component noise qualification and should be substituted by modal techniques. The dominating dipole sound sources are found in narrow areas around the vane leading edges and the rotor blade trailing edges. Because of the non-axisymmetric geometry, vane dipole source strengths become a function of circumferential position. The unsteady shedding of vortices from the vane suction surfaces is identified as a further possible source mechanism. However, the contributions of structural vibrations and mode scattering due to small manufacturing imperfections remain unclear.

scholarly journals Stability of Finite Difference Discretizations of Multi-Physics Interface Conditions

2013 ◽  
Vol 13 (2) ◽  
pp. 386-410 ◽  
Author(s):  
Björn Sjögreen ◽  
Jeffrey W. Banks
Keyword(s):  
Stokes Equations ◽  
Normal Mode Analysis ◽  
Linear Equations ◽  
Mode Analysis ◽  
Navier Stokes ◽  
Computational Domain ◽  
Interface Conditions ◽  
Step Size ◽  
Time Step ◽  
Time Step Size

AbstractWe consider multi-physics computations where the Navier-Stokes equations of compressible fluid flow on some parts of the computational domain are coupled to the equations of elasticity on other parts of the computational domain. The different subdomains are separated by well-defined interfaces. We consider time accurate computations resolving all time scales. For such computations, explicit time stepping is very efficient. We address the issue of discrete interface conditions between the two domains of different physics that do not lead to instability, or to a significant reduction of the stable time step size. Finding such interface conditions is non-trivial.We discretize the problem with high order centered difference approximations with summation by parts boundary closure. We derive L2 stable interface conditions for the linearized one dimensional discretized problem. Furthermore, we generalize the interface conditions to the full non-linear equations and numerically demonstrate their stable and accurate performance on a simple model problem. The energy stable interface conditions derived here through symmetrization of the equations contain the interface conditions derived through normal mode analysis by Banks and Sjögreen in [8] as a special case.

Transient Dynamic Analysis of Rotors Using SMAC Techniques: Part 2, Numerical Study

1992 ◽  
Vol 114 (4) ◽  
pp. 482-488 ◽  
Author(s):  
S. Ratan ◽  
J. Rodriguez
Keyword(s):  
Numerical Study ◽  
Time Domain Analysis ◽  
Superposition Method ◽  
Step Size ◽  
Time Step ◽  
Transient Dynamic Analysis ◽  
Transient Time ◽  
Rotor Systems ◽  
Time Step Size ◽  
And Performance

A new method for performing transient time-domain analysis of rotor systems using a Successive Merging and Condensation (SMAC) technique was introduced in Part 1. This approach can be applied to rotor analysis problems formulated with the finite element method. A numerical study, including examples, comparison of methods, and performance evaluation, is presented here. Validation and applicability of the SMAC method are illustrated with three examples: conservative, nonconservative, and nonlinear. The SMAC algorithm is then compared to the following methods: Transfer Matrix Method (TMM), Modal Superposition Method, and Runge-Kutta Method, and is demonstrated to be computationally more efficient in terms of CPU time and storage space. The issues of stability and time-step size are also studied.

scholarly journals Numerical Study on Catalytic Hydrodeoxygenation of Pyrolytic Bio-Oil Model Compound, Guaiacol, in Fluidized Bed Reactor

2021 ◽  
Author(s):  
Ogene Fortunate ◽  
Nanda Kishore
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Model Compound ◽  
Numerical Study ◽  
Thermochemical Conversion ◽  
Fluidised Bed ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Bio Oil

Abstract The bio-oil obtained by thermochemical conversion of lignocellulosic biomass consist of large fractions of oxygenated compounds which deteriorate its quality leading to low calorific value, high viscosity, high density, high moisture content, etc. Therefore, the bio-oil should be deoxygenated using hydrogen in the presence of appropriate catalyst to improve its properties. Adequate literature on pyrolysis of biomass within the framework of computational fluid dynamics is available but only a couple of papers available on hydrodeoxygenation of bio-oil obtained by pyrolysis. Thus, in this study, guaiacol has been selected as a representative model compound of phenolic fraction of bio-oil for upgrading it by catalytic hydrodeoxygenation. The reaction process has been implemented in a fluidised bed reactor in the presence of palladium catalyst, Pd/Al 2 O 3 using computational fluid dynamics (CFD) based solver, ANSYS Fluent 14.5. The range of conditions considered herein are: weight-hourly space velocity (WHSV) = 1, 3 and 5 h -1 ; superficial H 2 -gas velocity, u = 0.075, 0.15 and 0.25 m/s; catalyst load = 0.06 kg and temperature, T = 548 K, 573 K, and 598 K. The solver has been thoroughly validated in terms of grid dependence study, time step size dependence study validating hydrodynamics and HDO results wherever possible with existing literature results. The HDO of guaiacol produces phenol as the most abundant compound along with significant amount of cyclopentanone and methanol. The formation of cyclopentanone from HDO of guaiacol is favourable at high temperature whereas low temperature conditions favour formation of methanol and phenol.

Smoothed Profile Method for Particulate Two-Phase Flow

2008 ◽  
Author(s):  
Xian Luo ◽  
Martin R. Maxey ◽  
George E. Karniadakis
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Integration Scheme ◽  
Force Density ◽  
Step Size ◽  
Time Step ◽  
Element Discretization ◽  
Profile Method ◽  
Time Step Size ◽  
Smoothed Profile Method

We re-formulate and demonstrate a new method for particulate flows, the so-called “Smoothed Profile” method (SPM) first proposed in [1]. The method uses a fixed computational mesh, which does not conform to the geometry of the particles. The particles are represented by certain smoothed indicator profiles to construct a smooth body force density term added into the Navier-Stokes equations. The SPM imposes accurately and efficiently the rigid-body constraint inside the particles. In particular, while the original method employs a fully-explicit time-integration scheme, we develop a high-order semi-implicit splitting scheme, which we implement in the context of spectral/hp element discretization. We show that the modeling error of SPM has a non-monotonic dependence on the time step size Δt. The optimum time step size balances the thickness of the Stokes layer and that of the profile interface. Subsequently, we present several numerical simulations, including flow past three-dimensional complex-shaped particles and two interacting microspheres, which are compared against full direct numerical simulations and the force coupling method (FCM).

scholarly journals Numerical Study of a Francis Turbine over Wide Operating Range: Some Practical Aspects of Verification

2020 ◽  
Vol 12 (10) ◽  
pp. 4301
Author(s):  
Chirag Trivedi ◽  
Igor Iliev ◽  
Ole Gunnar Dahlhaug
Keyword(s):  
Numerical Model ◽  
Transport Model ◽  
Numerical Study ◽  
Operating Conditions ◽  
Francis Turbine ◽  
Step Size ◽  
Time Step ◽  
Angular Rotation ◽  
Time Step Size ◽  
Automatic Optimization

Hydropower plays an essential role in maintaining energy flexibility. Modern designs focus on sustainability and robustness using different numerical tools. Automatic optimization of the turbines is widely used, including low, mini and micro head turbines. The numerical techniques are not always foolproof in the absence of experimental data, and hence accurate verification is a key component of automatic optimization processes. This work aims to investigate the newly designed Francis runner for flexible operation. Unsteady simulations at 80 operating points of the turbine were conducted. The numerical model consisted of 16 million nodes of hexahedral mesh. A SAS-SST (scale adaptive simulation-shear stress transport) model was enabled for resolving/modeling the turbulent flow. The selected time-step size was equivalent to one-degree angular rotation of the runner. Global parameters, such as efficiency, torque, head and flow rate were considered for proper verification and validation. (1) A complete hill diagram of the turbine was prepared and verified with the reference case. (2) The relative error in hydraulic efficiency was computed and the over trend was studied. This allowed us to investigate the consistency of the numerical model under extreme operating conditions, far away from the best efficiency point. (3) Unsteady fluctuations of runner output torque were studied to identify unstable regions and magnitude of torque oscillations.

scholarly journals Multi-Degree of Freedom Propeller Force Models Based on a Neural Network and Regression

2020 ◽  
Vol 8 (2) ◽  
pp. 89 ◽  
Author(s):  
Bradford Knight ◽  
Kevin Maki
Keyword(s):  
Neural Network ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Open Water ◽  
Small Time ◽  
Training Data ◽  
Step Size ◽  
Time Step ◽  
Neural Network Approach ◽  
Time Step Size

Accurate and efficient prediction of the forces on a propeller is critical for analyzing a maneuvering vessel with numerical methods. CFD methods like RANS, LES, or DES can accurately predict the propeller forces, but are computationally expensive due to the need for added mesh discretization around the propeller as well as the requisite small time-step size. One way of mitigating the expense of modeling a maneuvering vessel with CFD is to apply the propeller force as a body force term in the Navier–Stokes equations and to apply the force to the equations of motion. The applied propeller force should be determined with minimal expense and good accuracy. This paper examines and compares nonlinear regression and neural network predictions of the thrust, torque, and side force of a propeller both in open water and in the behind condition. The methods are trained and tested with RANS CFD simulations. The neural network approach is shown to be more accurate and requires less training data than the regression technique.

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