Trang 1 GRADUATION PROJECTMAJOR: THERMAL ENGINEERING TECHNOLOGYNUMERICAL INVESTIGATION FLOW AND THERMAL CHARACTERISTICS INSIDE OF THE EJECTOR AT DIFFERENT OPERATING CONDITIONSINSTRUCTOR:
INTRODUCTION
Overview of ejector
Living conditions are increasing improved leading to the development of air conditioners Currently, air conditioning systems are very diverse, besides basic air conditioning systems such as local air conditioning systems, central air conditioning systems, water chillers Central air conditioning systemss type VRV traditional vapor compression were controlled by electricity, consuming fossil fuels However, this leads to air pollution and greenhouse gas emissions, and this poses a threat to the environment Therefore, ejector cooling technology and air conditioning have attracted much attention The ejector uses thermal energy as an input source, so it can be operated by solar or industrial waste heat sources and used as an air compressor With the refrigeration cycle, the spray cycle utilizes a much smaller, simpler and compact operating cost
The nozzle as a kind of waste heat recovery and exhaust gas pressure device has the advantages of simple structure, no moving parts, low maintenance cost It has great potential in many application areas, such as liquid pressure boosting, gas extraction, thermal refrigeration cycles and more Crude Oil Distillation, Petrochemical Process, Edible Oil Deodorization, Thermal ejector cooling cycle acting as a thermal compressor
Steam ejectors can be used to pull a vacuum with motive steam pressure as low as
5 pounds per square inch gauge (psig), higher pressures of 15 to 50 psig are more practical
The specific fluid that is suitable for an ejector dependent on various factors like the design of the ejector, the desired operating conditions and the application requirements Common fluids used in ejectors include steam, air, water, and various gases such as nitrogen or carbon dioxide It is essential to choose a fluid that is compatible with the ejector materials and can meet the desired performance criteria for the specific application
Figure 1.1: Flow diagram (a) and the photograph (b) of experimental apparatus for ejector performance test [1]
Refrigeration systems use ejector works on the principle of reverse cycle, but in this case, the refrigerant vapor compression is done by the ejector In principle, the ejector air conditioner can use any type of refrigerant, but now people often use water as the refrigerant.
Reasons for choosing the simulation
In this topic, we carried out a survey of the entrainment ratio and operating parameters such as pressure, temperature and velocity of the ejector device with compressible flow, high velocity and complex flow, so we selected simulation to perform Numerical simulation is a very useful and effective computational aid in difficult cases instead of expensive and time consuming experiments
When the ejector is used in the air conditioning systemss to evaluate the operation of the device, we need to pay attention to parameters such as: outlet pressure, gas-liquid flow, energy source pressure, size and operating parameters motion
To evaluate the effectiveness of ejectors, we have characteristics such as: entrainment ratio, compression ratio, efficiency, pressurre recovery, etc
Reasons for choosing the topic
The energy supplied to the air conditioning systemss plays an important role However, before the requirement of environmental protection and the depletion of fuel sources Therefore, maintaining the entrainment ratio of the ejector is considered as one of the solutions to improve the working efficiency of the cooling cycle by ejector It has great potential in many application areas, such as liquid pressure boosting, gas extraction, thermal refrigeration cycle, etc Through the problem mentioned above, we realized the importance of entrainment ratio To do that, we use the method: “Numerical investigation flow and thermal characteristics inside of the ejector device at different operating conditions”.
Purpose and tasks of the topic
Simulate the ejector with different input parameters from which to evaluate the performance and compare with the theoretical background of the device
- Compare simulation results with calculated results and simulation results according to the article
Object and scope of the study
The object of this study is the nozzle We changed the inlet flow parameters by changing mass flow rate of the motive flow between 0.084129 kg/s and 0.289219 kg/s and keeping the entrained flow unchanged with R134a used Simulation results show the change of temperature, pressure and velocity from inside the liquid, thereby evaluating the entrainment ratio of the ejector in the cycle and the direction of improvement In addition, we also presented the compression flow through the nozzle with three cases of Mach number = 1, Mach number < 1, Mach number > 1 and velocity, pressure, and temperature profiles from left to right to evaluate the change of parameters in the ejector
THEORETICAL BACKGROUND
Overview of steam ejector
In 1910, Leblanc introduced a cycle with a steam nozzle His setup allowed for a cooling effect to be produced using low-level energy Since steam was widely available at the time, so-called steam-jet refrigeration systems have become popular should be common in the air conditioning of large buildings and railway carriages.[3]
An ejector is a device used in various mechanical and engineering systems to remove or expel a fluid or gas from a particular space or systems It operates on the principle of creating a pressure difference to suck in and then discharge the fluid or gas The specific purpose and function of an ejector vary depending on its application Ejectors are used to remove non-condensable gases or vapors from the steam space or condenser to improve the overall efficiency of the systems.
Structure of the nozzle
A typical ejector consists of an ejector, suction chamber, mixing chamber and diffusion tube An ejector air conditioning systems is similar to an air conditioning systems with a compressor, in that the compressor is replaced by an ejector and a generator is used to provide heat for the ejector to operate
Figure 2.1: Structure of the nozzle [1]
Working principle
Based upon Bernoulli’s Principle, as the velocity of a fluid increases, its pressure decreases, and vice versa
An ejector works by accelerating a high-pressure stream (the ‘motive’) through a nozzle, converting the pressure energy into velocity Around the nozzle tip, where velocity is highest, a low-pressure region is created This is often called the suction chamber of the ejector Where the pressure in this region is lower than the pressure of the suction fluid connected to the ejector side-inlet or ‘suction branch’, it will be entrained/sucked into the body of the ejector The two fluid streams then travel through the diffuser section of the Ejector, where velocity is decreased as a result of the diverging geometry and pressure is regained When a nozzle works to evaluate its performance, we need to pay attention to the entrainment ratio, size and the most important internal medium is the entrainment ratio of the device
To investigate the ejector, there are important parameters to note such as geometric size, Witozinsky curve, length of mixing chamber, opening of mixing chamber
* Equation (1) is the desired equation which relates dA to du; it is called the area-velocity relation
With: A is area of cross-section
M is Mach number of cross-section u is the average velocity of cross-section
Equation (1) is very important; study it closely In the process, recall the standard convention for differentials; for example: a positive value of du connotes an increase in velocity, a negative value of du connotes a decrease in velocity, etc Equation (1) tells us the following information:
Figure 2.3: Compressible flow in converging and diverging ducts [3]
Imagine that we want to take a gas at rest and isentropically expand it to supersonic velocitys The above results show that we must first accelerate the gas subsonically in a convergent duct However, as soon as sonic conditions are achieved, we must further expand the gas to supersonic velocitys by diverging the duct Hence, a nozzle designed to achieve supersonic flow at its exit is a convergent-divergent duct, as sketched at the top of Figure 2.3 The minimum area of the duct is called the throat
Figure 2.4: Illustration and comparison of a supersonic nozzle and a supersonic diffuser [3]
1.For 0 ≤ M < 1 (subsonic flow), the quantity in parentheses in Equation (9) is negative Hence, an increase in velocity (positive du) is associated with a decrease in area (negative d A) Likewise, a decrease in velocity (negative du) is associated with an increase in area (positive d A) Clearly, for a subsonic compressible flow, to increase the velocity, we must have a convergent duct, and to decrease the velocity, we must have a divergent duct These results are illustrated at the top of Figure 2.4
2.For M > 1 (supersonic flow), the quantity in parentheses in Equation (1) is positive Hence, an increase in velocity (positive du) is associated with an increase in area (positive d A) Likewise, a decrease in velocity (negative du) is associated with a decrease in area (negative d A) For a supersonic flow, to increase the velocity, we must have a divergent duct, and to decrease the velocity, we must have a convergent duct
These results are illustrated at the bottom of Figure 2.4; they are the direct opposite of the trends for subsonic flow
3 For M = 1 (sonic flow), Equation (1) shows that d A = 0 even though a finite du exists Mathematically, this corresponds to a local maximum or minimum in the area distribution Physically, it corresponds to a minimum area, as discussed below.
Groups of parameters that affect the performance of the ejector
Systems operating parameters such as temperature, pressure, motive flow and entrained flow, back pressure directly affect the ejector operability and performance [4,5] followed by the influence of other parameters representing fluid flow characteristics such as compression coefficient, compositional composition, physical properties of fluid flow [6] The problem is to optimize the internal structure of the ejector device to achieve the highest performance.
Classification of nozzles
Ejector types divided into 2 mainly kind: based on flow and geometry
Figure 2.5: Single-phase steam ejector [7]
- Constant area mixing, constant pressure mixing
Figure 2.6: Convergent and convergent-divergent nozzle [8]
Advantages and disadvantages of ejector
- Available in a wide variety of materials
* How to improve ejector systems efficiency:
- Use proper sizing and design
Relevant studies
With some keywords like “ejector; steam ejector; a cooling use ejector” will give us many article results including an article about numerical ejector simulation Some examples can be taken as the scientific paper "Ejectors: applications in refrigeration technology" of authors including: Kanjanapon Chunnanond, Satha Aphornratana show about This article provides a literature review of nozzles and their applications in refrigeration, i.e., background and theory of nozzles and jet chiller cycles, performance characteristics, working fluids and improved beam refrigerators [24]
Another article by three writers including Pradeep Gupt, Pramod Kumar, Srisha M.V Rao is “Artificial neural network model for single-phase real gas ejectors” [25] presenting very complex fluid flow phenomena (including subsonic, ultrasonic, suffocation, shock waves, turbulence et al.) in a simple structure
An article by authors: Yulei Huang, Peixue Jiang, Yinhai Zhu titled "Quasi-two- dimensional ejector model for anode gas recirculation fuel cell systems" talks about the two-dimensional nozzle model and the flow phenomenon of boundary layer, shock line and mixing layer have been integrated It has been experimentally verified that the liquid mass flow test error of the nozzle designed by this new model is less than 15%, and simulation analysis has confirmed that the internal flow field matches the simulation results
Through these studies, we found that the ejector has a complex internal flow, diverse structure The influence of these parameters is very important to understand the nature of the strain, we consulted a report by authors: Xinyue Hao, Jiwei Yan, Neng Gao, Oleksii Volovyk, Yifan Zhou, Guangming Chen titled “Experimental
11 investigation of improved nozzles with optimal flow profile” [1] Specifically, this paper simulates an improved nozzle with an optimal flow profile according to the Witozinsky curve, which can better match the fluid flow characteristics than the conventional simple cone design proposal and research to reduce internal irreversible loss The detailed geometrical dimensions of the conventional nozzle and the improved nozzle under the design conditions are calculated based on the kinetic function of the gas The suction chamber and the convergence segment of the dynamic flow profile of the innovative nozzle designed according to the Witozinsky Ejector curve are used in refrigeration systems to increase the cooling efficiency In this simulation, we will use the mass flow rate motive flow input is 0.089219 kg/s and the entrained flow input is 0.044896 as mentioned in the article.
Related Formula
We will use the theoretical background that the paper provides and combine the theoretical from the book: “Fundamentals of Aerodynamics” for this part
Where ρ is the density and →is the velocity
2 (3) where τ is the stress tensor, μe is the dynamic viscosity, I is the unit tensor, i and j are space vector directions
E E P k T h J t ( ) e (4) where E is the total energy, ke is the effective thermal conductivity, h is the enthalpy, J is the diffusive flux of species
* Re is Reynolds number and is calculated by the formula:
In there: is the dynamic viscosity (Pa.s), is the density of the fluid (kg/m 3 ), dh is the hydraulic diameter (m), G is the mass flow rate (kg/s)
In there:is the density of the fluid (kg/m 3 ), dh is the hydraulic diameter (m)
* The performance of an ejector is measured by its entrainment ratio which is the mass flow rate ratio of the entrained flow to that of the motive flow It is given as:
ANSYS SOFTWARE AND CFD SIMULATION OVERVIEW
Introduction to numerical simulation CFD
* Introduction to CFD (Computational Fluid Dynamics):
Computational fluid dynamics (CFD) is a branch of fluid mechanics using numerical analysis and data structures to analyze and solve problems related to fluid flow Computers are used to perform the calculations necessary to simulate the free flow of liquids and the interaction of liquids ( liquids and gases ) with surfaces defined by boundary conditions With high-velocity supercomputers, better solutions can be achieved and are often required to solve the biggest and most complex problems Ongoing research yields software that improves the accuracy and velocity of complex simulation scenarios such as flow transition or turbulence flow Initial validation of such software is usually done by testing equipment such as a wind tunnel
In addition, analysis theoretical or previous empirical analysis of a particular problem can be used for comparison [9]
Figure 3.1: Wind velocity distribution in a parking tunnel (red shows the location with the highest velocity) [9]
To this day, the basics of CFD, if classified in terms of mathematical models, include elementary and turbulent flows inside and outside the object combustion reactive flow, compressible flow, heat transfer, multiphase flow with particles dispersed in continuous phase, continuous multiphase flow and phase separation surface,
14 interaction between flow and object under impact, multicomponent flow, and interaction between flow dynamics and molecular or magnetic motion
Figure 3.2: Basic model in CFD simulation [9]
* Practical applications of CFD simulation
Today it is difficult to find industry sectors without the presence of CFD simulations The most common applications of CFD simulation in industries can be classified into the following groups: aviation and aerospace industry: using simulation to optimize the wing profile (airfoil)
- Automotive industry: simulation of combustion reaction in an engine
- Construction industry: Simulation and optimization of heating (heating), ventilation (ventilation), and air conditioning (HVAC) – HVAC, and refrigeration systems
- Petroleum and Chemical Industry Systems: Reactor simulation (CSTR mixer, fluidized bed, bubble column, etc.), distillation tower
- Industrial equipment: Pumps, fans, compressors, turbines, and centrifugal separators (cyclones)
- Biomedical and pharmaceutical technology: Design of microfluidics, micromixing, and blood vessel simulation
- Weather and climate: Weather forecast
- Marine and shipbuilding: Modeling interaction between waves and hull stress, predictive model of hull resistance
Figure 3.3: Practical application of CFD [9]
The basic procedure when performing a CFD basic simulation is as follows:
- Step 2: Build geometry and process geometry on Workbench, Solid work or some other software
- Step 3: Mesh the model You can mesh structured or unstructured depending on the resource and the accuracy of the request result
- Step 5: Set up the solution method
- Step 8: If the mesh has converged, we perform simulations with different cases, process the results and generate reports
Figure 3.4: CFD basic simulation process
There are three methods that CFD often uses to discretize a systems of nonlinear equations into a systems of linear equations: the Finite Element Method (FEM), the finite volume method (FVM), the Finite Differences Method (FDM)
The finite element method (FEM) is a popular method for solving numerical differential equations that arise in engineering and mathematical modeling Typical problem areas of interest include the traditional areas of structural analysis, heat transfer, fluid flow, mass transport and electromagnetic potential
FEM is also a generalized numerical method for solving specific derivative equations in two or three spatial variables (that is, some boundary value problem ) To solve the problem, FEM breaks down a large systemss into smaller, simpler parts called finite elements
The finite volume method ( FVM ) is a method of representing and evaluating the partial derivative equation in the form of an algebraic equation [10] In the finite volume method, the volume integral in a partial differential equation containing the term divergence is converted to a surface integral , using the divergence theorem These terms are then evaluated as fluxes at the surfaces of each finite volume Since the flux entering a given volume is identical to the flux leaving the adjacent volume, these methods are conservative Another advantage of the finite volume method is that it is easily constructed to allow for unstructured meshes This method is used in many packages calculus of fluid dynamics "Finite volume" refers to the small volume around each node on the mesh
This is a digital method to solve differential equations by approximating the derivative with a finite difference Both the space and time domains (if any) are discretized to a finite number of steps, and the values of the solutions at these discrete points are approximated by solving algebraic equations containing finite finite differences and values from neighboring points The finite difference method converts ordinary or partial differential equations, which may be nonlinear, into a systemss of linear equations that can be solved using matrix algebraic techniques Modern computers that can perform these linear algebra calculations efficiently, together with their ease of implementation, have led to their wide application in numerical simulation today [10].
Introduction of Ansys Workbench software
ANSYS is a comprehensive software that covers almost all areas of physics, helping to enter the world of virtual modeling and engineering analysis for the design stages Most investors love this technical analysis software for what it does and how much it costs them
This powerful analysis software takes the engineering design process to a new level, not only working with variable environments, parameters, multi-level functions, but also supporting adaptive working with new engineering models, but CAE tools many features Of course, Ansys will help improve design efficiency, enhance creativity,
18 reduce constraints, physical limitations, perform simulation tests that cannot be performed on other software
ANSYS Workbench has many modules and sub software inside To link modules together and easily link tasks, there is a common platform that is ANSYS Workbench However, with this simulation, we will mainly implement the following 4 modules: ANSYS Design Modeler, ANSYS Meshing, ANSYS Fluent, CFD Post In which ANSYS Design Modeler is the module we have to contact first in building geometric models of objects Next is ANSYS Meshing to do the modeling work Then will perform Setup of boundary conditions and run simulation with ANSYS Fluent Finally, use CFD Post to export and process simulation results
Figure 3.6: ANSYS workbench interface Depending on the problem requirements, there are many options such as Electric, Modal, Fluid Flow (CFX), For this topic, we will use Fluid Flow (Fluent) to simulate the fluid flow in the nozzle The figure below shows the interface of Fluent
Figure 3.7: Fluid flow (Fluent) interface
To perform the simulation, we need to take the first step of building the geometry with Geometry In this step, we can do it directly on Workbench or use another way to
20 import the model that we have built in other software such as AutoCAD, Solid work, etc We need to pay attention to the size of the model carefully to draw accurately otherwise when performing simulation calculations will occur deviation
Figure 3.8: ANSYS design modeler interface
The model building by ANSYS Design Modeler is done in 3D space with 3 different planes including: XY plane, YZ plane, ZX plane This interface is designed to be minimalistic and has specific images that make it easy for users to grasp In this section, users can build 2D or 3D models from simple to complex
Besides, Ansys also has the function to support commands to simplify drawing and save more time To build the model, we use the following commands:
Figure 3.9: Commands to build geometry
After building the geometry, the next step is meshing using ANSYS Meshing The interface in this grid is also quite simple and easy to understand, the commands are described by pictures To mesh the model, select the "Generate" icon, the software will automatically mesh but it will be an unstructured mesh
This mesh does not meet the requirements to run the simulation, so it is necessary to use other tools It is very important that the mesh meets the standards for simulation large in simulation
Meshing for the model is quite important, fine mesh and standard mesh structure will help us simulate calculations much more accurately and save a lot of time
After performing meshing, we will set up boundary conditions for the model and run the simulation All will be done on ANSYS Fluent In the interface of ANSYS Fluent, there are many folders that we need to pay attention to such as: General, Models, Materials, Cell Zone Conditions,
Figure 3.11: Commands when performing Setup
- The General command is used to set the method of running the simulation
- The Model’s command is used to activate the energy equation and select the flow model for simulation problems such as k-epsilon, k-omega, etc
- The Materials command selects and sets the parameters of the materials used for the model
- The Cell Zone Condition command selects the area where the corresponding material type is set in Materials
- The Boundary Condition statement is used to set boundary conditions
- The Solution command gives us options for the software to calculate and run the simulation
- The Result command will give us the results of the simulation in the form of data or graphs
Meshing Overview
Meshing is the process in which the continuous geometric space of an object is subdivided into thousands or more shapes to determine the correct physical shape of the
24 object The more detailed the mesh, the more detailed the 3D CAD model will be the more precise, allowing for high fidelity simulation Meshing also known as meshing, is the process of creating a two and three dimensional mesh; it divides complex geometries into elements that can be used to discretize a domain Since meshing often consumes a significant portion of the time to obtain simulation results, the meshing tools automatically Advanced dynamics can provide faster and more accurate solutions
Figure 3.13: Some common types of mesh [12]
3.3.2 The quality evaluation factors of the mesh
There are many ways to verify that the model mesh is acceptable One of them is to conduct research on mesh independence Although studying mesh independence is great, it requires a considerable amount of time – you need a lot of models with eyes grid and different results Also, research is often best done for specific regions of the model rather than looking at the whole world Fortunately, there are a number of tools in ANSYS that allow us to quantify the overall mesh quality in (and after) the grid generation stage If you look at Grid -> Stats -> Grid Metrics, you will find a drop-down menu as shown in the image below There are many ways we can check the quality of the grid However, people often use one of the following parameters: Smoothness, Skewness and Orthogonal Quality
Figure 3.15: ANSYS mesh metric recommendations [13]
In a nutshell, the aspect ratio is the ratio between the longest length of the cell to the shortest length The ideal aspect ratio is 1 The smaller the ratio, the higher the quality of an element The calculation method varies by cell type as follows:
- Hexagon Aspect Ratio: The ratio of the maximum side length to the minimum side length
- Aspect Ratio tetrahedron: It correlates the maximum side length and the radius of the sphere inside the cell
Figure 3.16: Compare high and low aspect ratio per element type [14]
Skewness aka obliqueness, obliqueness is one of the main quality measures of a mesh The obliqueness determines how far the mesh is from the ideal level
Figure 3.17: Ideal obliques of the mesh [12]
Highly skewed faces and cells is unacceptable because the equations being solved assume that the cells are relatively equal/next to each other
The two methods for measuring deviation are:
- Based on the volume of the tetrahedron (only applicable to triangles and tetrahedra)
- Based on deviations from normalized angles This method applies to all cell and face shapes, e.g., pyramids and prisms The default offset method for triangles and tetrahedra is the regular volume method
In a high-quality mesh, the dimensions between adjacent faces or cells must be smooth and gradual Large size differences between adjacent faces or cells will result in a poorly computed grid because the differential equations are solved assuming that the cells shrink or grow smoothly
Figure 3.18: Fine mesh and non-fine mesh [15]
There are two different ways of creating a mesh:
- Structured (also known as Grids):
In essence, creating a structural grid is to find a coordinate transformation to arrange objects from heterogeneous, non-orthogonal physical space (x, y, z) to orthogonal computational space ( ξ, η, ζ ) in turn in the order: Determine the distribution of the boundary points,Determine the distribution of the points inside the object
The biggest advantage of unstructured mesh is that it can fit almost any geometry However, the meshing process is not fully automated and requires considerable user interaction to produce a mesh with an acceptable level, while greatly reducing element distortion
Figure 3.19: Structured and unstructured grids [16]
Orthogonal Quality is a metric used in mesh learning and numerical simulation to evaluate the quality of a computational mesh It measures the degree of angle between the grid lines in the calculated grid Orthogonal gridlines mean that the grid lines intersect at right angles
The higher the orthogonal quality, i.e., the closer the grid lines are to each other, the more accurate and stable the calculated grid A good orthogonal quality ensures that flows, gradients and other phenomena are more accurately simulated in the computed mesh
To evaluate the quality of an orthogonal, several metrics are commonly used, including the angle between grid lines, the ratio of angles, the ratio of the minimum angles, and the skewness index The orthogonal quality can also be applied to 3D meshes, where the orthogonality of the mesh faces is measured Orthogonal quality is important in building accurate and efficient computational meshes for numerical simulation in fields such as fluid dynamics, gas dynamics, and thermodynamics
ANSYS Fluent offers two solutions, Pressure or Density The Density solution method is a density-based solution, and the Pressure method is a pressure-based method
Initially, the Pressure method was only suitable for incompressible streams but was later developed for use in compressible streams When solving the problem of compressible or incompressible flow, we can use one of these two methods However, in general if the problem is liquid flow, we use the Pressure method, and if the problem is related to gas flow we use the Density method
In essence, the motion of turbulent flow is unstable Therefore, to solve the systemss of equations in the case of turbulent flow, people often use a method as follows
There are many turbulent flow models, but the most popular today are the k-ε and k-ω models Currently, the k-ε and k-ω models have become the industry realizable models that are widely used for most fluid flows in engineering problems
The k-ε model deals with two variables: k, entangled kinetic energy; and ε (epsilon), the turbulent kinetic energy dissipation rate Wall functions are used in this model, so the flow in the buffer zone is not simulated The k-ε model was previously very popular for industrial applications due to its good convergence velocity and relatively low memory requirements It does not accurately calculate flow fields exhibiting adverse pressure gradients, strong curvatures of flow, or jet flow It performs well for external flow problems around complex geometries.
MODEL BUILDING AND SIMULATIONS
Geometry
In this project, we built a model using SolidWorks software and consulted the scientific article [1] We designed the shape and size of the tube to match the size used in the article
Solid works is a powerful 3D design software and integrates with many supporting tools diverse, so it is very trusted by engineers At the same time, the software is widely applied in fields from: construction, pipeline, architecture, interior,
Over many versions, Solid works has made many outstanding strides in features, performance as well as meeting the expectations of professional 3D drawing design needs for engineering and industrial sectors
Figure 4.1: SolidWorks software [17] o Advantages of SolidWorks
- Powerful tools, quick processing of blueprints
- Design and assemble parts into finished products
- Intuitive interface, easy to use
- The ejector model is drawn from Solidworks as shown below:
Figure 4.3: Simple scheme of ejector in millimeters
The structure of the improved nozzle by the Witozinsky curve [1] is shown in Figure 4.3 compared with the conventional nozzle With such a model, we set the flow rate for the motive flow is 0.089219 kg/s at 75 0 C Celsius and the entrained flow is 0.044896 kg/s at 15 0 C
Table 4.1: Key dimensions of the test ejector
Throat diameter of motive nozzle 3.8
Outlet diameter of motive nozzle 4.5
Axial length of converging segment of motive nozzle 4.1
Inlet diameter of cylindrical mixing chamber 9.6
Length of cylindrical mixing chamber 70
Inlet diameter of suction chamber d2 32
Axial length of suction chamber 28
Distance between nozzle exit and mixing chamber inlet 9
The difference between the traditional model and the model using the Witozinsky curves:
- Traditional Geometry: an ejector using its traditional geometry and rules It focuses on modeling the shape and size of ejector components, including tubes, nozzles, diffusers, etc Pressure, flow and efficiency parameters are calculated based on this geometric model
- Geometry with Witozinsky curve: an ejector using the Witozinsky curve model, a special method for determining the pressure distribution in the ejector Instead of focusing solely on the shape and size of the components, this approach delves into the effect of pressure on ejector performance The Witozinsky curve is used to simulate the pressure distribution and optimize the parameters needed to achieve the best performance
Both of these methods have their own advantages and limitations Traditional geometry methods are often simpler and easier to understand but may omit some important parameters Meanwhile, the geometry method with the Witozinsky curve provides more detailed information about the pressure distribution but requires more sophisticated analysis and knowledge to apply
The essence of the Witozinsky method is to reduce boundary layer decoupling during CFD (Computational Fluid Dynamics) simulation This is a method in CFD to minimize inaccurate digitization of areas of interference or separation between objects in the simulation space
The benefit of reducing boundary layer decoupling reduces distortion and error in simulation results When there is separation between boundary layers, interaction phenomena between objects are not simulated correctly This can lead to unreliable and misleading results By reducing boundary layer decoupling, we can increase the accuracy and reliability of the CFD simulation
Figure 4.4: Schematic diagram of Witozinsky curve
Figure 4.5: Flow profile of suction chamber and converging segment of nozzle
As shown in Figure 4.5, these improvement curves are taken from the reference article, the front part of the Witozinsky curve is faster contraction, which is conducive to flow velocity improvement Meanwhile, due to the slower contraction of the rear part, uniformity and stability of fluid are better at exit, and turbulence effect is relatively low Flow profile designed according to the Witozinsky curve can not only reduce the flow resistance loss but also avoid the boundary layer separation This is valuable guidance for the design of ejector for improving efficiency It expressed formula of Witozinsky curve in figure 4.4 as:
Where, r∗ is the exit height of converging segment; R is the entrance height of converging segment; L is the axial distance of converging segment; x is the distance from the entrance of converging segment; r is the height of position x.
Meshing
For the generated model, meshing is done with the help of Ansys Meshing tool The mesh used for the entire model is unstructured The mesh quality evaluation criteria are Element Quality, Aspect Ratio, Jacobian Ratio, Jacobian Ratio, Gauss Point, Warping
Factor, Parallel Deviation, Maximum Corner Angle, Skewness, Orthogonal Quality, Characteristic Length Fluent software is most interested in 2 indicators: Skewness and Orthogonal Quality
Figure 4.6: ANSYS grid metric recommendations [16]
During the simulation, my team created many meshes with different number of elements However, my team selected 3 best quality meshes with not too large number of elements to save time and resources, used on the computer when performing the simulation From there, a suitable mesh can be selected to perform the simulation
Table 4.2: Table of evaluation criteria of created grids
Mesh Elements Orthogonal Quality Skewness
To achieve the most accurate simulation results, we changed the element size of the grid to evaluate the grid more optimally and efficiently This is also an important issue in the steps of performing a simulation
Following table 4.2 to evaluate the quality of the above mesh among all the created meshes, based on the mesh quality evaluation index, it is found that the 3 generated meshes have quite good mesh quality, showing the ability of the grid to converge when run will be higher and will be used to run simulation As shown on the above grid quality evaluation index, all 3 selected grids have the index Orthogonal Quality and Skewness are all in the level of being rated as good and very good as shown in the picture 4.6 This shows that the possibility of convergence when conducting simulation will be better
Mesh M1: Figure 4.8 is over 1 million elements, the index Orthogonal Quality and
Skewness are all in the level of being rated as good
Mesh M2: Figure 4.9 is approximately 1.3 million elements the index Orthogonal
Quality and Skewness are all in the level of being rated as good
Mesh M3: Figure 4.10 is approximately 1.7 million elements, the index Orthogonal
Quality and Skewness are all in the level of being rated as good.
Simulation parameters
Simulation state : choose state Steady Transient flow is an unstable flow, i.e it is time dependent Steady flow (or established flow) is not time dependent, it is steady flow Transient is synonymous with Unsteady
Solution method (Solver) : using the solution method based on density (Density –
Based) used for compressible flows
Gravity : choose according to the direction of the design model, for example, the model is built on the OXZ axis with the direction of gravity in the Y axis, then we will choose Y = -9.81
Energy : the simulation device uses a temperature source, so we have to turn on the energy equation
Viscous : we choose the realizable k- model→ Enhanced wall streatment
Depending on the purpose of simulation and flow to choose the setting parameter
Figure 4.12: The realizable k- model settings
In this part, we used R134a for the ejector to evaluate its performance
Table 4.3: Properties of saturated vapor R134a at 15 o C [18]
We will be replacing materials in this section We select the region and click Edit: R134a
Figure 4.14: Cell zone conditions setting
Calculate the hydraulic diameter of the entrained and motive inlets:
Based on the simulation results of the article [1], scientists have studied the ejector device operating with the motive flow rate of 0.089219 kg/s at 75 0 C, the entrained flow is 0.044896 kg/s at 15 0 C and the output is 0.134115 kg/s So, we will simulate the device with the flow of the inputs and increase or decrease the flow to match the design and simulation conditions
Mass Flow Rate Temperature Hydraulic Diameter kg/s O C m
Mass flow out (outlet) 0.134118 (kg/s)
Figure 4.15: Mass flow rate setting
We choose the solution to suit the model and the simulation purpose
Set convergence for simulation: to simulate the most accurate results, we should set convergence parameters for it, depending on each simulation having its own convergence requirements Here, we set parameter 1e-06 to make the mesh easier to converge and save computation time
Mesh convergence
After running the simulation with the same boundary conditions, we continues to consider the convergence of the mesh to select the most objective mesh to perform the calculation and compare the results in a more optimal way to avoid wasting simulation time and minimize errors in the calculation process We will rely on the velocity profile and residual index of the refrigerant flow inside the device We can understand residual in mathematics called double error It is a criterion to evaluate the convergence of the computational diagram in the calculation method For each iteration step, the double error will be calculated to adjust and correct how the next "step" is to ensure the fastest calculation velocity while ensuring the stability and convergence of the calculation scheme In the CFD simulation, a remainder equal to 10 -4 is considered loosely convergent, a level of 10 -5 is considered to be well converged, and a level of 10 -6 onwards is considered to be closely converged In push we will create a line with coordinates (48,0,0) with (48,4.8,0) to draw the velocity profile of each mesh case
Figure 4.18: Line position on ejector
Figure 4.19: Residual index of the grid M1
Figure 4.20 shows Residual index of grid M1 after running the simulation starting from the 350 iteration onwards, the lines have tended to be horizontal showing convergence characteristics
Figure 4.21: Residual index of the grid M2
Similar to the M1 grid Figure 4.22 shows Residual index of grid M2 after running the simulation starting from the 300 iteration onwards, the lines have tended to be horizontal showing convergence characteristics
Figure 4.23: Residual index of the grid M3
In this grid, there is a difference with 2 grids M1 and M2 Figure 4.24 shows Residual index of grid M1 after running the simulation starting from the 450 iteration onwards, the lines have tended to be horizontal showing convergence characteristics
Select the appropriate mesh based on the velocity profile
Based on the residual plot of the 3 grids, it can be seen that all 3 grids tend to converge Because the profiles gave nearly identical results with relatively small differences, it was difficult to compare them, so we pooled the velocity curves together to select the mesh for the simulation
Figure 4.25: Mesh convergence results based on velocity profile
Based on the results of the velocity profile gathered into one, we can see that all 3 grids have good convergence, but M2 mesh has the best convergence efficiency, so we decided to choose M2 (1285639 elements) grid to conduct simulation and evaluate the results of the device
RESULTS AND DISCUSSION
Characteristics of the flow in ejector
First, we choose to investigate the flow and thermal characteristics of the ejector with the following parameters: the motive flow and entrained flow are 0.089219 kg/s and 0.044896 kg/s, respectively, the mass flow out is 0.134115kg/s and the temperature is 75 O C at motive flow and 15 O C at entrained flow
After finishing the simulation, we create planes at locations with different to see the change in temperature, pressure and velocity of the liquid inside
Case 2 will be presented with simulation and specific details of the flow
(a) Figure 5.1a: The velocity of the refrigerant inside the device (m/s)
In Figure 5.1a, shows the contour of the cross-sectional velocity distribution of the ejector device Looking at the legends on the figure, we can see that the velocity at the input is 132.88767 m/s, then increases to 343.91971 m/s at the throat position with narrow cross-section converges and then exits at the diverging end has a value of 97.58025 m/s in the mixing chamber and eventually drops to 13.993696 m/s at the outlet Looking at these numbers, we can observe the velocity changes that occur during the process inside the ejector From the inlet to the throat, there is a significant increase
50 in velocity, creating a pressure drop and enhancing the ejector's efficiency However, after the mixing chamber, there is a significant decrease in velocity, resulting in a low value at the outlet This could be attributed to the mixing process and the interaction between the liquid in the ejector These parameters provide important information for understanding and improving the performance of ejectors in real-world applications
Figure 5.1b: Line position along the ejector
Figure 5.1c: Velocity magnitude of x-axis in ejector Figure 5.1c provides a visual representation of the velocity profile of the ejector along the x-axis, focusing on the cross-sectional analysis Initially, the input velocity is maintained at approximately 127 m/s until it reaches the position of 28 mm, known as the throat of the ejector
At this point, there is a sudden increase in velocity to around 335 m/s Subsequently, the velocity sharply decreases until it reaches the position of 40 mm, just before the inlet of the mixing chamber Afterward, the velocity gradually decreases uniformly until it reaches the output position of the device
Figure 5.1d: Velocity of nozzle flow
Figure 5.1e: Velocity passing through throat
As can be seen in Figure 5.1e the velocity after entering the throat tends to increase at the position of the smallest cross-section and decrease until the inlet of
52 the mixing chamber The entry velocity at position P1 is 170 m/s, then increases and reaches the maximum value at P2 with a velocity of 335 m/s and gradually decreases to 263 m/s at section P3
Figure 5.2a: The pressure of the refrigerant inside the device (Pascal)
As can be seen in Figure 5.2a, it shows the distribution of the circulating pressure in the device which reaches its maximum value at the inlet then drops suddenly at the throat position and gradually increases again to the outlet position
In Figure 5.2a, the pressure at the inlet reaches the maximum value of 530 kPa, then gradually decreases to -443 kPa at the throat position and gradually increases to -258 kPa at the mixing chamber and finally continues to increase to 113 kPa at the outlet increased nearly 4 times compared to the pressure in the mixing chamber Looking at these numbers, we can observe the pressure change occurring during the process inside the nozzle From the inlet to the throat, the pressure increases dramatically However, there is a sudden decrease in pressure before entering the throat position and then gradually increasing again until the outlet position This may be due to agitation and interaction between the fluid flows in the nozzle
Figure 5.2b: Pressure magnitude of x-axis in ejector
Figure 5.2b depicts the pressure distribution of the ejector across the x-axis, specifically analyzing a cross-sectional view The input pressure is maintained steadily around 450 kPa until it reaches a certain location, approximately 28 mm at throat along the x-axis At this point, there is a sudden drop in pressure to -540 kPa, and subsequently, it gradually increases towards a position of 40 mm, just before the inlet of the mixing chamber Finally, the pressure continues to gradually rise as it moves towards the output of the ejector device
Figure 5.2c: Pressure of nozzle flow
Looking at Figure 5.2c, there is a very abrupt change in pressure from the starting point of Plane 1 to Plane 3
The pressure reached its maximum value at the inlet with 452231.08 Pa then dropped to the bottom -687212.97 Pa at the throat and gradually increased to -53227,155 Pa at the outlet
Figure 5.2d: Pressure passing through throat
In Figure 5.2d, the pressure after entering the throat tends to decrease gradually at the position of the smallest cross-section and gradually increase until the inlet of the mixing chamber The inlet pressure at position P1 is 300 kPa then decreases and reaches the minimum value at P2 with a pressure of -550 kPa and gradually increases to -50 kPa at cross section P3
Figure 5.3a: The temperature of the refrigerant inside the device ( o C)
In Figure 5.3a, the temperature at the inlet reaches the maximum value at 75 o C, then decreases to 66.68 o C at the throat position and continues to gradually decrease to 30.26 o C at the mixing chamber and finally has the lowest value of 19.31 o C in the output Looking at these numbers, we can observe the temperature change occurring during the process inside the nozzle From the inlet to the throat, there is a negligible drop in temperature However, after coming out of the nozzle the temperature gradually decreases towards the output of the device
Figure 5.3b: Temperature magnitude of x-axis in ejector Figure 5.3b show the temperature distribution along the x-axis The graph illustrates that the input temperature decreases from 75 o C to 68 o C, a position roughly 58 mm inside the mixing chamber no significant temperature change occurs Subsequently, the temperature continues to gradually decrease towards the output of the device This temperature profile provides insights into the thermal behavior within the ejector, aiding in optimizing its performance and efficiency
Figure 5.3c: Temperature of nozzle flow
Figure 5.3d: Temperature passing through the throat Figure 5.3d depicts the internal temperature with the position of section P1 having a temperature of 66( o C) and gradually increasing towards the P2 plane with 67( o C) and P3 decreasing to 66.5( o C) As can be seen the temperature rise and fall is not stable inside the tube
Table 5.2: Average pressure and velocity results at the cross-sections Case 2
Area-Weighted Average Statics Pressure
Figure 5.4: Isentropic subsonic nozzle flow of Case 2
Figure 5.5: Streamlines show velocity inside
Figure 5.5 the velocity of the fluid is represented by the flow lines and the fluid path as the velocity from the inlet to the outlet Velocity color distribution lines of internal fluid At the inlet the velocity does not change appreciably but when coming right at the throat the velocity increases significantly and decreases towards the ejector output Looking at the cross section right at the throat we can see that there is separation of the boundary layer
Figure 5.6: Vector field of internal flow
In Figure 5.6, the velocity of the fluid is represented by flow lines representing the fluid's path as velocity from inlet to outlet At the inlet, the velocity of the fluid does not change much but after reaching the throat increases greatly and gradually decreases towards the outlet after exiting the nozzle This could be attributed to the mixing process and the interaction between the liquid in the ejector These parameters provide important information for understanding and improving the performance of ejectors
* Cross section at large gradient (select at throat):
Figure 5.7: Contour of velocity at throat (m/s) Figure 5.7 shows the contour of the cross-section with a large gradient, the velocity data changes corresponding to the color with the largest velocity at the center of 331 m/s and decreasing to 231 m/s and 99.2 m/s, respectively
Figure 5.8: Contour of pressure at throat (Pascal) Figure 5.8 shows the contour of a face with a large gradient, the pressure data changes in proportion to the color of the section
Flow characteristic at different cases
Figure 5.42: Set value ranges for faces First, we create 3 cross-sections right at the converging with coordinates P1(28,0,0), P2(32,1,0,0) and P3(39,0,0) like the creation steps survey plane
In Figure 5.44 after creating a plane at the selected location, we change the parameters of velocity, pressure, etc to create the surface we want to survey
5.3.1 Export the result to draw the line of the subsonic nozzle flow
Based on the parameters after running the simulation, we generates the isentropic subsonic nozzle flow graph
Figure 5.45: Location of three sections
Then we select 3 instances 1 2 3 of the graph entrainment ratio to continue plotting to assess the flow
The equation calculate the Mach number:
is the average velocity magnitude (m/s)
K represents the texture coefficient of the substance
T is the temperature (in degrees Kelvin)
Figure 5.46: Velocity and pressure at the cross-section P1
Figure 5.47: Velocity and pressure at the cross-section P2
Figure 5.48: Velocity and pressure at the cross-section P3
Figure 5.49: Velocity and pressure at the cross-section P1
Figure 5.50: Velocity and pressure at the cross-section P2
Figure 5.51: Velocity and pressure at the cross-section P3
Figure 5.52: Velocity and pressure at the cross-section P1
Figure 5.53: Velocity and pressure at the cross-section P2
Figure 5.54: Velocity and pressure at the cross-section P3
Table 5.14: Average pressure and velocity results at the cross-sections Case 2
Area-Weighted Average Statics Pressure
Figure 5.55: Isentropic subsonic nozzle flow of Case 2
- The pressure reaches its maximum value at the inlet with 452231.08 Pa then drops to the bottom -687212.97 Pa at the throat and gradually increases to -53227.155 at the outlet
- Velocity starts at 138.32947 m/s, continues to increase to 339.88413 at throat then decreases to 247.37038 m/s at outlet
Table 5.15: Average pressure and velocity results at the cross-sections Case 3
Area-Weighted Average Statics Pressure (Pa) 672388.57 -921455.13 -61312.841 Area-Weighted Average Velocity Magnitude
Figure 5.56: Isentropic subsonic nozzle flow of Case 3
- The pressure reached its maximum value at the inlet with 672388.57 Pa then dropped to the bottom -921455.13 Pa at the throat and gradually increased to -61312.841 Pa at the outlet
- Velocity starts at 162.48004 m/s, continues to increase to 400.30317 m/s at throat then drops to 288.26585 m/s at outlet
Table 5.16: Average pressure and velocity results at the cross-sections Case 4
Area-Weighted Average Statics Pressure (Pa) 918841 -1310450 -94001 Area-Weighted Average Velocity Magnitude
95 Figure 5.57: Isentropic subsonic nozzle flow of Case 4
- The pressure reached its maximum value at the inlet with 918841 Pa then dropped to the bottom -1310450 Pa at throat and gradually increased to
- Velocity starts at 193.28 m/s, continues to increase to 474.76 m/s at the throat then decreases to 316.81 m/s at the outlet
* From the above three cases, we can draw a graph Isentropic subsonic nozzle flow
Figure 5.58: Isentropic subsonic nozzle flow
Figure 5.58a consider the convergent-divergent nozzle sketched Consider the duct shown in Figure 5.58 Assume that sonic flow exists at the throat, where the area is A ∗ The Mach number and the velocity at the throat are denoted by M ∗ and u ∗ , respectively Since the flow is sonic at the throat, M ∗ = 1 and u ∗ = a ∗
At any other section of this duct, the area, the Mach number, and the velocity are denoted by A, M, and u, respectively, as shown in Figure 5.65 Writing Equation between A and A∗, we have: ρ ∗ u ∗ A ∗ = ρu A (14)
Figure 5.58b consider magnitude velocity with the velocities changing to throat from 339m/s, 400m/s, 474.76m/s ( case2, case3 and case4 ) respectively, tending to decrease to 247m/s, 288m/s, 316m/s
Figure 5.59: Geometry for the derivation of the area–Mach number relation
Figure 5.59b shows the local Mach number will increase slightly through the convergent portion, reaching a maximum value at the throat with Me,1 = 1.17, Me,2= 1 and Me,3 = 0.9, as shown by curve This Mach number at the throat will not be sonic; rather, it will be some small subsonic value Downstream of the throat, the local Mach number will decrease in the divergent section, reaching a very small but finite value
A : cross-sectional area of nozzle outlet
A * : cross-sectional area at throat
Figure 5.58c shows the pressure in the convergent section will gradually decrease from p0 at the inlet to a minimum value at the throat with an approximate ratio of -1.52 in all three case, and then will gradually increase to the value pe,1 at the exit
From Figure 5.59 and the figure showing the Mach number, the pressure ratio of the convergent-divergent nozzle in the theoretical background we can clearly see:
- The number of Mach from the 3 cases of 1, 2 and 3 tends to be almost similar when compared with each other
- Meanwhile, the pressure ratio of the simulation tends to decrease much more significantly and exhibits sub-negative values
Figure 5.60: Isentropic subsonic nozzle flow of theoretical background
After running the simulation, the outlet pressure value of Case 1 to Case 6 is 221.9 (kPa), 251.533 (kPa), 373.697 (kPa), 552.996 (kPa), 610.553 (kPa) and 646.905 (kPa) respectively, within the range suitable for the outlet pressure gauge is the Druck PTX
Besides, the motive flow inlet of this study is at least 0.084219 kg/s for Case 1 and maximum motive flow inlet of 0.289219 kg/s for Case 6, within the allowable article range of 0-0.302 kg/s in table 4 [1]
With the above parameters and result, therefore it can be determined that these results are compatible with the systemss using ejector similar to the one in the article
CONCLUSION AND RECOMMENDATION
Conclusion
As the demand for cooling systems increasing, research and development of equipment related to exhaust gas reuse becomes more and more necessary
The research subject of this essay, we focuses on the research object is the steam ejection and the compares with the theoretical background, CFD simulation the of the steam ejector device with the parameters presented in chapter 4 and the analysis results
By analyzing the flow characteristics, the study has achieved the following results:
- Characteristics of the flow in steam ejector
- Investigate the influence of mass flow inlet
- Export result draw the line of the subsonic nozzle flow
Recommendation
We discovered that the ANSYS software was quite heavy, which made meshing for the model and simulation quite time-consuming This was true during we are simulation, analysis, and comparison of output cases Consequently, we suggest the following measures for solving the issue:
- Time and effort can be saved by setting up a standard model for the paper and simulation
- Temperature, pressure, velocity, and flowrate are significant values for a high- accuracy comparison and should be noted when choosing the setting parameters
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