代做EG501V/EG503G Computational Fluid Dynamics Final CFD Assignment 2023/24代做C/C++程序

2024-07-15

EG501V/EG503G (2023/24)

EG501V/3G – Computational Fluid Dynamics

Assignment 2023/24 (Resit)

Final CFD Assignment (2023/24,Resit)

1) Write a report containing the summary of all performed numerical simulations. The report has the format of a scientiﬁc paper and a templates (in MS Word and LaTeX) can be found in MyAberdeen.

2) The report should contain up to 8 pages including bibliography and appendices (for any extra-page, there will be a penalty of 0.5 CGS/page). The report should have the following structure:

(a) Title

(b) Abstract, which should contain

• Motivation;

• Aims and objectives of the work, and;

• Main ﬁndings.

(c) Introduction: overview of models (i.e., conservative ﬂow equations, turbulence models etc) used in the simulations and the relevance of the ﬂow past a (heated) cylinder as a validation experiment for CFDs;

(d) Simulation setup: List of all relevant information with respect to geometry, mesh, initial and boundary conditions, reference values, turbulence models etc;

(e) Results and detailed analysis (based on fundamental ﬂuid dynamics and references);

(f) Concluding remarks;

(g) Bibliography.

3) Marking Criteria:

(a) Presentation and style (20%): this covers (i) general presentation (design and presentation of ﬁgures and tables, quality of written text, all expected sections are present etc), (ii) abstract, (iii) introduction and (iv) conclusions and recommendations;

(b) Description of simulations setup (10%);

(d) Task B (30%): values for Cd and Nu and discussion.

Note: As stated above, marks are distributed based on results (values, tables and plots as stated in the Tasks) and critical analysis of the results (discussion).

4) Prepare the report as a PDF ﬁle and submit it through MyAberdeen by Friday, July 19th 2024,at noon (BST).

5) Late submission: Students must seek the approval of the Mitigating Circumstances Committee (MCC) for extensions. Where extensions are not granted by the MCC the following penalties will apply:

i) Up to 24 hours late, the grade will be deducted by 2 Common Grading Scale (CGS) points;

ii) For each subsequent day, up to a maximum of seven days total, the grade will be deducted by a further CGS point for each day, or part of a day, up to a maximum of seven days late;

iii) Over seven days late, a grade of G3 will be awarded.

Full documentation for the current late submission penalty policy can be found in

https://www.abdn.ac.uk/staffnet/teaching/key-education-policies-for-students- 11809.php#panel13739

6) Note that the submitted work is part of the continuous assessment which will contribute in 50% to your EG501V/503Ggrade.

1 Motivation

High-density polyethylene (HDPE) is the third largest plastic commodity produced in the world (after PVC and PP) with annual production of 51.33 MMT (2016) and worth of approximately USD 64 billions. HDPE resin is used in a wide range of applications from food and beverage packaging to corrosion- and thermal-resistant pipes. There are several industrial patented technology processes to produce HDPE worldwide, e.g., Chevron-Philips slurry loop, Lyondell-Basell Ziegler slurry process, Dow Chemical solution process, Univation’s UNIPOL swing process (Fig. 1) etc.

Prior to the removal of water and oxygen at the pressure vessel, gaseous ethylene (75。C; stream A of Fig. 1) is heated up to 140。C in a ﬁnned tube cross-ﬂowheat exchanger (HEx, Fig. 2). Fluid ﬂowing in the tubes is mineral oil (Therminol 66) at 300。. After contaminants (water and oxygen) removal, the gaseous stream is refrigerated from 120。C to 90。C in a similar ﬁnned tube cross-ﬂow HEx (stream G, same mineral oil was used, but with temperature of 50。C).

In order to support the design of such heat exchangers, speciﬁc technical information must be obtained:

i) heat transfer from the tubes to the gaseous stream (stream A);

Figure 1: Gas Phase LLDPE/HDPE (Dow Chemical swing process) ﬂowchart.

ii) turbulence-induced mixing and heat transfer enhancement in HEx.

2 Introduction to Model Quality Assurance

In the design and optimisation of any CFD model for processes and equipment (e.g., heat exchang- ers, pressure vessels, engines etc), it is critical to obtain reliable information about ﬂow dynamics (i.e., spatial- and time-distribution of pressure, temperature and velocity), and how the geometry can im- pact on them. Therefore, a systematic investigation is necessary to ensure the reliability of model. Such investigation is often called model quality assurance (QA).

Model and software quality assurance encompass a set of procedures adopted by the CFD industry to en- sure that models and software are in compliance with fundamental requirements, such as accuracy, range of conﬁdence etc [1]. Model and software QA are the main means to assess the accuracy of com-

Figure 2: Simpliﬁed sketch of a section of the ﬁnned tube cross-ﬂowheat exchange.

putational simulations and they comprise of two sets of procedures [2]:

1. Veriﬁcation is a “process of determining that a model implementation accurately represents the developer’s conceptual description of the model and the solution to the model”;

2. Validation is a “process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended uses of the model”;

Veriﬁcation and validation (V&V) procedures are critical tools to build conﬁdence of numerical simula- tions. Before simulating ﬂow and heat dynamics in HEx A, a V&V procedure should be designed to assess the initial accuracy of the model.

3 Model Validation 1: Flow Past a Cylinder

3.1 Introduction

Theﬂow past a cylinder problem is a a classical CFD V&V exercise as it addresses several ﬂuid mechanics phenomena relevant to engineering applications. For example, boundary layer separations and oscilla- tory ﬂows in the region behind the cylinder are due to shedding vortices at moderate and high Reynolds numbers (Re). Such ﬂows behaviour may result in structural vibrations in equipment and, potentially, structural damage.

At low Re , any perturbation in the velocity boundary conditions is readily dissipated by viscous forces. However, as Re increases, such perturbations may lead to ﬂuid instabilities at the wake of the cylin-

(c)

Figure 3: Flow past a cylinder: (a) numerical simulation at Re = 140 by [3] and (b) experiments by [4]; (c) summary of ﬂow regimes over a cylinder (extracted from [5]).

der (also known as ’vortex shedding’), which may strongly impact on both ﬂuid velocity and pressure distributions and, therefore on momentum and heat transfers. More background information on the classic ﬂow past a cylinder problem can be found in ﬂuid mechanics textbooks which are available online through the library (e.g., [6,7]).

This problem is also relatively simple to reproduce in laboratory and experimental data can be readily compared against numerical simulations over a range of Re conditions (Fig. 3). Therefore, numerical simulations of the ﬂow past a cylinder problem are useful to:

a) assess numerical accuracy (veriﬁcation) and functionalities of models as the ﬂow is steady and sym- metric at low Re and;

b) validate the model against experimental results [8,9,10,11].

3.2 Numerical Simulations

As a ﬁrst step for V&V of the numerical model embedded in the ANSYS Fluent, let’sperform numerical simulations of the classic ﬂow past a cylinder experiments (Fig.4). In this numerical experiment, we will assume that the working ﬂuid is air at room conditions. Also, the problem is simpliﬁed by assuming that the cylinder is at constant temperature, i.e., we should neglect the ﬂow in the pipe.

Figure 4: Flow past a cylinder: sketch of computational domain. Note that the sketch is not made in-scale.

Air is assumed to behave as an incompressible ﬂuid and dimensions of the computational domain are (see Fig. 4):

D = 2.5 cm L = 31.5 cm L1 = 11.5 cm L2 = 12.5 cm H = 25.0 cm.

3.2.1 Procedure for Building the Geometry & Mesh

In order to create the geometry in DesignModeller, draw a rectangular domain around the origin and then draw within the domain a circle with the origin as its centre. Give the appropriate dimensions and then create a surface from your sketch. As we are dealing with a complex 2D ﬂow dynamics, the mesh will be unstructured. In Mesher, change the method to Triangles. The default mesh is rather coarse, so you can specify the mesh sizing along the cylinder. You can control the mesh size in the ﬂow domain in the mesh size setting (Details view). By changing element size will allow to control the mesh (you can try out other settings as well, an example of mesh reﬁnement setup can be seen in Fig.5). Then, either:

a) For mixed structured (near the cylinder) and unstructured (anywhere else) mesh: you can apply Inﬂation to the wall of the cylinder (which will create a structured mesh around the cylinder with better control of layers of mesh grid), or;

b) For fully unstructured mesh: you may use theReﬁnement option.

Figure 5: Snapshot of mesh reﬁnement control.

3.2.2 Solution Solver

1. The top and bottom wall of the domain can be set to no shear boundary conditions (i.e., no ﬂux across the borders);

2. For the ’pressure velocity coupled scheme’ solver, you should use the SIMPLE method;

3. For the transient regime, you should solve the problem using PISO method;

4. All transient simulations should be conducted with 10 iterations per time-step;

5. Drag and lift coefﬁcient monitors can be set under Report Deﬁnitions. Give them sensible names and ensure to tick Report ﬁle, Report Plot and Print to console. Under Monitors you can change the ﬁlename and path for the output ﬁles and the setting for the plots. For transient simulations it is useful to get, and plot, data every timestep (instead of every iteration);

6. Bear in mind that numerical simulations may take 10-50 mins to run (depending on the mesh resolu- tion and turbulence model);

7. For assessing mesh-independent solution, there are two methodologies that can be used:

i) Visual inspection (qualitative assessment) of ux × y plots (in a similar way that you have done in previous Practicals) of several simulations with continuous mesh reﬁnement, and/or;

ii) From ux × y plots from two continuous mesh reﬁnements,i and i + 1, extract ux(i)(y) and ux(i)+1 (y)

(both are arrays of dimension N), calculate

A solution is assumed to be mesh-independent if ε is smaller than a prescribed value, e.g., 10-5 ≤ ε ≤ 10-1 . As we want to capture the vortex dynamics during the instabilities, a good practice in this test-case is to assess the velocity ( 7i-7ii above) at approximately ‘from 1 to 3 diameters’ away from the cylinder (i.e., not at the outlet region).

iii) For making line (i.e., XY) plots of simulated ﬁelds around the cylinder, in the CFD-Results:

i) Select Location → Polyline;

ii) ‘Boundary Intersect‘ in Method;

iii) ’symmetry’ in Boundary List;

iv) ’cylinder’ in Intersect with.

iv) Although you do not need to show (in the report) plots and screen-shots on tests for veriﬁcation (e.g., mesh-independent solution, solution convergence, mass conservation, Y+ for the turbulent ﬂow simulations etc), you should perform. all these tests as any failure may result in poor drag and heat transfer predictions.

8. Turbulence models: simulations performed with Re = 104 (only) should use both:

i) k-∈ model and;

ii) Transition SST model [12,13].

Simulation time (for V2022R1) for completion varies from approximately 8-12 min (k-E) and 25-50 min (SST) for ~60k mesh grid resolution.

4 Model Validation 2: Flow Past a Heated Cylinder

The next stage in the model and software QA is to assess the accuracy of the heat and ﬂow dynamic models through another classic test-case – ﬂow past a heated cylinder (see Section 7.4 of [14] and Sections 6.1-3 of [15]). The model setup (introduced in Section 3.2) must be validated against both experimental and simulated data (some useful data can be found in [16,17,18,19,20,21], but other references maybe sought for further data).

As simulated and experimental data from these (and other) references are often based on air ﬂow around a heated cylinder under various Reynolds (Re) and Prandtl (Pr) conditions, you should conduct the model validation using air at 75。C with Re = 104 . Use the computational domain designed in Section 3.1with the cylinder at constant temperature of 300。C. Finally, assume that the ﬂuid’s density depends only on the temperature.