Fluid Dynamics and Balance Equations for Reacting Flows
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Stall/Surge Dynamics of a Multi-Stage Air Compressor in Response to a Load Transient of a Hybrid Solid Oxide Fuel Cell-Gas Turbine System
Journal of Power Sources 365 (2017) 408e418 Contents lists available at ScienceDirect Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour Stall/surge dynamics of a multi-stage air compressor in response to a load transient of a hybrid solid oxide fuel cell-gas turbine system * Mohammad Ali Azizi, Jacob Brouwer Advanced Power and Energy Program, University of California, Irvine, USA highlights Dynamic operation of a hybrid solid oxide fuel cell gas turbine system was explored. Computational fluid dynamic simulations of a multi-stage compressor were accomplished. Stall/surge dynamics in response to a pressure perturbation were evaluated. The multi-stage radial compressor was found robust to the pressure dynamics studied. Air flow was maintained positive without entering into severe deep surge conditions. article info abstract Article history: A better understanding of turbulent unsteady flows in gas turbine systems is necessary to design and Received 14 August 2017 control compressors for hybrid fuel cell-gas turbine systems. Compressor stall/surge analysis for a 4 MW Accepted 4 September 2017 hybrid solid oxide fuel cell-gas turbine system for locomotive applications is performed based upon a 1.7 MW multi-stage air compressor. Control strategies are applied to prevent operation of the hybrid SOFC-GT beyond the stall/surge lines of the compressor. Computational fluid dynamics tools are used to Keywords: simulate the flow distribution and instabilities near the stall/surge line. The results show that a 1.7 MW Solid oxide fuel cell system compressor like that of a Kawasaki gas turbine is an appropriate choice among the industrial Hybrid fuel cell gas turbine Dynamic simulation compressors to be used in a 4 MW locomotive SOFC-GT with topping cycle design. -
CFD Based Design for Ejector Cooling System Using HFOS (1234Ze(E) and 1234Yf)
energies Article CFD Based Design for Ejector Cooling System Using HFOS (1234ze(E) and 1234yf) Anas F A Elbarghthi 1,*, Saleh Mohamed 2, Van Vu Nguyen 1 and Vaclav Dvorak 1 1 Department of Applied Mechanics, Faculty of Mechanical Engineering, Technical University of Liberec, Studentská 1402/2, 46117 Liberec, Czech Republic; [email protected] (V.V.N.); [email protected] (V.D.) 2 Department of Mechanical and Materials Engineering, Masdar Institute, Khalifa University of Science and Technology, Abu Dhabi, UAE; [email protected] * Correspondence: [email protected] Received: 18 February 2020; Accepted: 14 March 2020; Published: 18 March 2020 Abstract: The field of computational fluid dynamics has been rekindled by recent researchers to unleash this powerful tool to predict the ejector design, as well as to analyse and improve its performance. In this paper, CFD simulation was conducted to model a 2-D axisymmetric supersonic ejector using NIST real gas model integrated in ANSYS Fluent to probe the physical insight and consistent with accurate solutions. HFOs (1234ze(E) and 1234yf) were used as working fluids for their promising alternatives, low global warming potential (GWP), and adhering to EU Council regulations. The impact of different operating conditions, performance maps, and the Pareto frontier performance approach were investigated. The expansion ratio of both refrigerants has been accomplished in linear relationship using their critical compression ratio within 0.30% accuracy. The results show that ± R1234yf achieved reasonably better overall performance than R1234ze(E). Generally, by increasing the primary flow inlet saturation temperature and pressure, the entrainment ratio will be lower, and this allows for a higher critical operating back pressure. -
Derivation of Fluid Flow Equations
TPG4150 Reservoir Recovery Techniques 2017 1 Fluid Flow Equations DERIVATION OF FLUID FLOW EQUATIONS Review of basic steps Generally speaking, flow equations for flow in porous materials are based on a set of mass, momentum and energy conservation equations, and constitutive equations for the fluids and the porous material involved. For simplicity, we will in the following assume isothermal conditions, so that we not have to involve an energy conservation equation. However, in cases of changing reservoir temperature, such as in the case of cold water injection into a warmer reservoir, this may be of importance. Below, equations are initially described for single phase flow in linear, one- dimensional, horizontal systems, but are later on extended to multi-phase flow in two and three dimensions, and to other coordinate systems. Conservation of mass Consider the following one dimensional rod of porous material: Mass conservation may be formulated across a control element of the slab, with one fluid of density ρ is flowing through it at a velocity u: u ρ Δx The mass balance for the control element is then written as: ⎧Mass into the⎫ ⎧Mass out of the ⎫ ⎧ Rate of change of mass⎫ ⎨ ⎬ − ⎨ ⎬ = ⎨ ⎬ , ⎩element at x ⎭ ⎩element at x + Δx⎭ ⎩ inside the element ⎭ or ∂ {uρA} − {uρA} = {φAΔxρ}. x x+ Δx ∂t Dividing by Δx, and taking the limit as Δx approaches zero, we get the conservation of mass, or continuity equation: ∂ ∂ − (Aρu) = (Aφρ). ∂x ∂t For constant cross sectional area, the continuity equation simplifies to: ∂ ∂ − (ρu) = (φρ) . ∂x ∂t Next, we need to replace the velocity term by an equation relating it to pressure gradient and fluid and rock properties, and the density and porosity terms by appropriate pressure dependent functions. -
MSME with Depth in Fluid Mechanics
MSME with depth in Fluid Mechanics The primary areas of fluid mechanics research at Michigan State University's Mechanical Engineering program are in developing computational methods for the prediction of complex flows, in devising experimental methods of measurement, and in applying them to improve understanding of fluid-flow phenomena. Theoretical fluid dynamics courses provide a foundation for this research as well as for related studies in areas such as combustion, heat transfer, thermal power engineering, materials processing, bioengineering and in aspects of manufacturing engineering. MS Track for Fluid Mechanics The MSME degree program for fluid mechanics is based around two graduate-level foundation courses offered through the Department of Mechanical Engineering (ME). These courses are ME 830 Fluid Mechanics I Fall ME 840 Computational Fluid Mechanics and Heat Transfer Spring The ME 830 course is the basic graduate level course in the continuum theory of fluid mechanics that all students should take. In the ME 840 course, the theoretical understanding gained in ME 830 is supplemented with material on numerical methods, discretization of equations, and stability constraints appropriate for developing and using computational methods of solution to fluid mechanics and convective heat transfer problems. Students augment these courses with additional courses in fluid mechanics and satisfy breadth requirements by selecting courses in the areas of Thermal Sciences, Mechanical and Dynamical Systems, and Solid and Structural Mechanics. Graduate Course and Research Topics (Profs. Benard, Brereton, Jaberi, Koochesfahani, Naguib) ExperimentalResearch Many fluid flow phenomena are too complicated to be understood fully or predicted accurately by either theory or computational methods. Sometimes the boundary conditions of real-world problems cannot be analyzed accurately. -
Continuity Equation in Pressure Coordinates
Continuity Equation in Pressure Coordinates Here we will derive the continuity equation from the principle that mass is conserved for a parcel following the fluid motion (i.e., there is no flow across the boundaries of the parcel). This implies that δxδyδp δM = ρ δV = ρ δxδyδz = − g is conserved following the fluid motion: 1 d(δM ) = 0 δM dt 1 d()δM = 0 δM dt g d ⎛ δxδyδp ⎞ ⎜ ⎟ = 0 δxδyδp dt ⎝ g ⎠ 1 ⎛ d(δp) d(δy) d(δx)⎞ ⎜δxδy +δxδp +δyδp ⎟ = 0 δxδyδp ⎝ dt dt dt ⎠ 1 ⎛ dp ⎞ 1 ⎛ dy ⎞ 1 ⎛ dx ⎞ δ ⎜ ⎟ + δ ⎜ ⎟ + δ ⎜ ⎟ = 0 δp ⎝ dt ⎠ δy ⎝ dt ⎠ δx ⎝ dt ⎠ Taking the limit as δx, δy, δp → 0, ∂u ∂v ∂ω Continuity equation + + = 0 in pressure ∂x ∂y ∂p coordinates 1 Determining Vertical Velocities • Typical large-scale vertical motions in the atmosphere are of the order of 0. 01-01m/s0.1 m/s. • Such motions are very difficult, if not impossible, to measure directly. Typical observational errors for wind measurements are ~1 m/s. • Quantitative estimates of vertical velocity must be inferred from quantities that can be directly measured with sufficient accuracy. Vertical Velocity in P-Coordinates The equivalent of the vertical velocity in p-coordinates is: dp ∂p r ∂p ω = = +V ⋅∇p + w dt ∂t ∂z Based on a scaling of the three terms on the r.h.s., the last term is at least an order of magnitude larger than the other two. Making the hydrostatic approximation yields ∂p ω ≈ w = −ρgw ∂z Typical large-scale values: for w, 0.01 m/s = 1 cm/s for ω, 0.1 Pa/s = 1 μbar/s 2 The Kinematic Method By integrating the continuity equation in (x,y,p) coordinates, ω can be obtained from the mean divergence in a layer: ⎛ ∂u ∂v ⎞ ∂ω ⎜ + ⎟ + = 0 continuity equation in (x,y,p) coordinates ⎝ ∂x ∂y ⎠ p ∂p p2 p2 ⎛ ∂u ∂v ⎞ ∂ω = − ⎜ + ⎟ ∂p rearrange and integrate over the layer ∫p ∫ ⎜ ⎟ 1 ∂x ∂y p1⎝ ⎠ p ⎛ ∂u ∂v ⎞ ω(p )−ω(p ) = (p − p )⎜ + ⎟ overbar denotes pressure- 2 1 1 2 ⎜ ⎟ weighted vertical average ⎝ ∂x ∂y ⎠ p To determine vertical motion at a pressure level p2, assume that p1 = surface pressure and there is no vertical motion at the surface. -
COMSOL Computational Fluid Dynamics for Microreactors Used in Volatile Organic Compounds Catalytic Elimination
COMSOL Computational Fluid Dynamics for Microreactors Used in Volatile Organic Compounds Catalytic Elimination Maria Olea 1, S. Odiba1, S. Hodgson1, A. Adgar1 1School of Science and Engineering, Teesside University, Middlesbrough, United Kingdom Abstract Volatile organic compounds (VOCs) are organic chemicals that will evaporate easily into the air at room temperature and contribute majorly to the formation of photochemical ozone. They are emitted as gases from certain solids and liquids in to the atmosphere and affect indoor and outdoor air quality. They includes acetone, benzene, ethylene glycol, formaldehyde, methylene chloride, perchloroethylene, toluene, xylene, 1,3-butadiene, butane, pentane, propane, ethanol, etc. Source of VOCs emission include paints, industrial processes, transportation activities, household products such as cleaning agents, aerosols, fuel and cosmetics. Catalytic oxidation is one of the most promising elimination techniques for VOCs as a result of it flexibility and energy saving. The catalytic materials enhance the chemical reactions that convert VOCs (through oxidation) into carbon dioxide and water. Removal of volatile organic compounds at room temperature has always been a challenge to researchers. Developing a catalyst which could completely oxidize the VOCs at very low temperature in order to avoid catalyst deactivation and promote energy saving has been the key focus among researchers in the recent years. Moreover, as the oxidation reaction is highly exothermic, the use of catalytic microreactors instead of packed bed reactors was considered. Microreactors are microfabricated catalytic chemical reactors with at least one linear dimension in the micrometer range. Usually, they consist of narrow channels and exhibit large surface area-to- volume ratios which leads to high heat and mass transfer properties. -
Chapter 3 Newtonian Fluids
CM4650 Chapter 3 Newtonian Fluid 2/5/2018 Mechanics Chapter 3: Newtonian Fluids CM4650 Polymer Rheology Michigan Tech Navier-Stokes Equation v vv p 2 v g t 1 © Faith A. Morrison, Michigan Tech U. Chapter 3: Newtonian Fluid Mechanics TWO GOALS •Derive governing equations (mass and momentum balances •Solve governing equations for velocity and stress fields QUICK START V W x First, before we get deep into 2 v (x ) H derivation, let’s do a Navier-Stokes 1 2 x1 problem to get you started in the x3 mechanics of this type of problem solving. 2 © Faith A. Morrison, Michigan Tech U. 1 CM4650 Chapter 3 Newtonian Fluid 2/5/2018 Mechanics EXAMPLE: Drag flow between infinite parallel plates •Newtonian •steady state •incompressible fluid •very wide, long V •uniform pressure W x2 v1(x2) H x1 x3 3 EXAMPLE: Poiseuille flow between infinite parallel plates •Newtonian •steady state •Incompressible fluid •infinitely wide, long W x2 2H x1 x3 v (x ) x1=0 1 2 x1=L p=Po p=PL 4 2 CM4650 Chapter 3 Newtonian Fluid 2/5/2018 Mechanics Engineering Quantities of In more complex flows, we can use Interest general expressions that work in all cases. (any flow) volumetric ⋅ flow rate ∬ ⋅ | average 〈 〉 velocity ∬ Using the general formulas will Here, is the outwardly pointing unit normal help prevent errors. of ; it points in the direction “through” 5 © Faith A. Morrison, Michigan Tech U. The stress tensor was Total stress tensor, Π: invented to make the calculation of fluid stress easier. Π ≡ b (any flow, small surface) dS nˆ Force on the S ⋅ Π surface V (using the stress convention of Understanding Rheology) Here, is the outwardly pointing unit normal of ; it points in the direction “through” 6 © Faith A. -
THERMODYNAMICS, HEAT TRANSFER, and FLUID FLOW, Module 3 Fluid Flow Blank Fluid Flow TABLE of CONTENTS
Department of Energy Fundamentals Handbook THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW, Module 3 Fluid Flow blank Fluid Flow TABLE OF CONTENTS TABLE OF CONTENTS LIST OF FIGURES .................................................. iv LIST OF TABLES ................................................... v REFERENCES ..................................................... vi OBJECTIVES ..................................................... vii CONTINUITY EQUATION ............................................ 1 Introduction .................................................. 1 Properties of Fluids ............................................. 2 Buoyancy .................................................... 2 Compressibility ................................................ 3 Relationship Between Depth and Pressure ............................. 3 Pascal’s Law .................................................. 7 Control Volume ............................................... 8 Volumetric Flow Rate ........................................... 9 Mass Flow Rate ............................................... 9 Conservation of Mass ........................................... 10 Steady-State Flow ............................................. 10 Continuity Equation ............................................ 11 Summary ................................................... 16 LAMINAR AND TURBULENT FLOW ................................... 17 Flow Regimes ................................................ 17 Laminar Flow ............................................... -
Performance Evaluation of Multipurpose Solar Heating System
Mechanics and Mechanical Engineering Vol. 20, No. 4 (2016) 359{370 ⃝c Lodz University of Technology Performance Evaluation of Multipurpose Solar Heating System R. Venkatesh Department of Mechanical Engineering Srinivasan Engineering College Perambalur, Tamilnadu, India V. Vijayan Department of Mechanical Engineering K. Ramakrishnan College of Technology Samayapuram, Trichy, Tamilnadu, India Received (29 May 2016) Revised (26 July 2016) Accepted (25 September 2016) In order to increase the heat transfer and thermal performance of solar collectors, a multipurpose solar collector is designed and investigated experimentally by combining the solar water collector and solar air collector. In this design, the storage tank of the conventional solar water collector is modified as riser tubes and header and is fitted in the bottom of the solar air heater. This paper presents the study of fluid flow and heat transfer in a multipurpose solar air heater by using Computational Fluid Dynamics (CFD) which reduces time and cost. The result reveals that in the multipurpose solar air heater at load condition, for flow rate of 0.0176 m3/s m2, the maximum average thermal efficiency was 73.06% for summer and 67.15 % for winter season. In multipurpose solar air heating system, the simulated results are compared to experimental values and the deviation falls within ± 11.61% for summer season and ± 10.64% for winter season. It proves that the simulated (CFD) results falls within the acceptable limits. Keywords: solar water collector, solar air collector, fluid flow, heat transfer and Compu- tational fluid dynamics. 1. Introduction Solar energy plays an important role in low{temperature thermal applications, since it replaces a considerable amount of conventional fuel. -
CONTINUITY EQUATION Another Principle on Which We Can Derive a New Equation Is the Conservation of Mass
ESCI 342 – Atmospheric Dynamics I Lesson 7 – The Continuity and Additional Equations Suggested Reading: Martin, Chapter 3 THE SYSTEM OF EQUATIONS IS INCOMPLETE The momentum equations in component form comprise a system of three equations with 4 unknown quantities (u, v, p, and ). Du1 p fv (1) Dt x Dv1 p fu (2) Dt y p g (3) z They are not a closed set, because there are four dependent variables (u, v, p, and ), but only three equations. We need to come up with some more equations in order to close the set. DERIVATION OF THE CONTINUITY EQUATION Another principle on which we can derive a new equation is the conservation of mass. The equation derived from this principle is called the mass continuity equation, or simply the continuity equation. Imagine a cube at a fixed point in space. The net change in mass contained within the cube is found by adding up the mass fluxes entering and leaving through each face of the cube.1 The mass flux across a face of the cube normal to the x-axis is given by u. Referring to the picture below, these fluxes will lead to a rate of change in mass within the cube given by m u yz u yz (4) t x xx 1 A flux is a quantity per unit area per unit time. Mass flux is therefore the rate at which mass moves across a unit area, and would have units of kg s1 m2. The mass in the cube can be written in terms of the density as m xyz so that m x y z . -
Overview of the Entropy Production of Incompressible and Compressible fluid Dynamics
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by PORTO Publications Open Repository TOrino Politecnico di Torino Porto Institutional Repository [Article] Overview of the entropy production of incompressible and compressible fluid dynamics Original Citation: Asinari, Pietro; Chiavazzo, Eliodoro (2015). Overview of the entropy production of incompressible and compressible fluid dynamics. In: MECCANICA. - ISSN 0025-6455 Availability: This version is available at : http://porto.polito.it/2624292/ since: November 2015 Publisher: Kluwer Academic Publishers Published version: DOI:10.1007/s11012-015-0284-z Terms of use: This article is made available under terms and conditions applicable to Open Access Policy Article ("Public - All rights reserved") , as described at http://porto.polito.it/terms_and_conditions. html Porto, the institutional repository of the Politecnico di Torino, is provided by the University Library and the IT-Services. The aim is to enable open access to all the world. Please share with us how this access benefits you. Your story matters. (Article begins on next page) Meccanica manuscript No. (will be inserted by the editor) Overview of the entropy production of incompressible and compressible fluid dynamics Pietro Asinari · Eliodoro Chiavazzo Received: date / Accepted: date Abstract In this paper, we present an overview of the Keywords Thermodynamics of Irreversible Processes entropy production in fluid dynamics in a systematic (TIP) · Compressible fluid dynamics · Incompress- way. First of all, we clarify a rigorous derivation of ible limit · Entropy production · Second law of the incompressible limit for the Navier-Stokes-Fourier thermodynamics system of equations based on the asymptotic analy- sis, which is a very well known mathematical technique used to derive macroscopic limits of kinetic equations 1 Introduction and motivation (Chapman-Enskog expansion and Hilbert expansion are popular methodologies). -
1 the Continuity Equation 2 the Heat Equation
1 The Continuity Equation Imagine a fluid flowing in a region R of the plane in a time dependent fashion. At each point (x; y) R2 it has a velocity v = v (x; y; t) at time t. Let ρ = ρ(x; y; t) be the density of the fluid 2 −! −! at (x; y) at time t. Let P be any point in the interior of R and let Dr be the closed disk of radius r > 0 and center P . The mass of fluid inside Dr at any time t is ρ dxdy: ZZDr If matter is neither created nor destroyed inside Dr, the rate of decrease of this quantity is equal to the flux of the vector field −!J = ρ−!v across Cr, the positively oriented boundary of Dr. We therefore have d ρ dxdy = −!J −!N ds; dt − · ZZDr ZCr where N~ is the outer normal and ds is the element of arc length. Notice that the minus sign is needed since positive flux at time t represents loss of total mass at that time. Also observe that the amount of fluid transported across a small piece ds of the boundary of Dr at time t is ρ−!v −!N ds. Differentiating under the integral sign on the left-hand side and using the flux form of Green’s· Theorem on the right-hand side, we get @ρ dxdy = −!J dxdy: @t − r · ZZDr ZZDr Gathering terms on the left-hand side, we get @ρ ( + −!J ) dxdy = 0: @t r · ZZDr If the integrand was not zero at P it would be different from zero on Dr for some sufficiently small r and hence the integral would not be zero which is not the case.