Engineering System Modelling & Simulation (ENG741) Coursework II

**Coursework Report Specification**

You are required to submit a report for the coursework. All necessary calculation procedures and diagrams should be listed and plotted. You should present the simulation results with discussion and comments. The report should be about 2500 words in length. It is suggested that your written report should contain the following elements.

**Introduction****Problem description****Calculation of flow parameters / characteristic stresses****Numerical implementation****Results and discussion****Concluding remarks****References**

Note: University regulations apply regarding late or non-submission of coursework. This assignment carries 50% of the total module marks.

**Handing in date: ****25 ^{th} January 2019**

#### Case Study 1: Hot water flow through a spiral groove circular pipe

Heat transfer enhancement is the process of improving the performance of a heat transfer system by increasing the heat transfer coefficient. Heat transfer enhancement technology has been developed and widely applied to heat exchanger applications; for example, refrigeration, automotives, process industry, chemical industry etc. A large number of attempts have been made to reduce the size and costs of the heat exchangers. An increase in heat transfer coefficient generally leads to another advantage of reducing the temperature driving force, which increases the second law efficiency, and decreases entropy generation. Among many techniques (both passive and active) investigated for augmentation of heat transfer rates inside circular tubes, tube fitted with full length twisted tape inserts (also called as swirl flow device) or having spiral grooves have been shown to be very effective in enhancing the heat transfer. A great deal of experimental works on heat transfer augmentation studies using twisted tape have been reported in the literature. The aim of this assignment is to model fluid flow and heat transfer augmentation for a circular tube having a regularly spaced spiral groove using CFD, which enable us to find out Nusselt number, friction factor for the given flow rates and the best ratio of the spiral groove depth to its pitch.

As shown in Figure 1, hot water flows through a spiral grooved circular pipe, made of structural steel, with the internal diameter *D*, the length of spiral groove part; *L* and the pitch *T*. The depth and width of the spiral groove are the same and designated as *W*. When hot water flows through the spiral groove circular tube, the flow inside the tube will be significantly affected by the spiral grooves. It can be anticipated that the hydrodynamics and heat transfer behaviour in the tube will be influenced due to the flow perturbation caused the spiral grooves. The spiral grooves will promote and generate turbulence in the vicinity of the tube internal surface, resulting in an enhancement of heat transfer and a larger pressure drop.

**Figure C1. Hot water flows through a spiral groove circular pipe**

For estimation of the pressure drop for flow through the spiral groove circular tube, the tube can be approximated as a long circular pipe. The friction coefficient *f* (also referred to as the Darci friction factor) can be calculated based on the Darci-Weisbach equation:

(1)

where *D* is the tube diameter, *r* is the density and *L* is the tube length. *Dp* represents the pressure drop along the tube and *U _{in}* is the mean velocity at the inlet. When water flows through a smooth circular pipe with

*Re*< 10

_{D}^{5}, the friction coefficient can be estimated using the Blasius equation:

(2)

For heat transfer, the following empirical correlations can be used for estimation of the Nusselt number.

Smooth tube: (Dittus-Bolter equation) (3)

Spiral groove tube: (4)

where *Nu* is the Nusselt number, defined as

(5)

and Pr is referred to as Pranlt number, defined as

(6)

where *a* is the heat transfer coefficient, *m* is the fluid dynamic viscosity and *l* is the thermal conductivity of the fluid. Thus, we can assess the flow resistance characteristics and heat transfer behaviour of the spiral groove circular tube by comparing the results using the above formulae.

The following conditions are given:

The spiral groove circular tube internal diameter *D* = 20 mm;

The total length of the tube *L _{total}* = 400 mm;

The length of the spiral grooves *L* = 200 mm;

The depth and width of the spiral groove *W* = 4 mm;

The spiral groove pitch *T* = 10 mm;

The temperature of the hot water at the inlet of the tube Tin = 100 °C.

The properties of hot water are assumed to be:

(1) The density of hot water *r* = 1000 kg/m^{3};

(2) The heat capacity *c _{p}* = 4182 J/kg×K;

(3) The thermal conductivity *l* = 0.6 W/mK;

(4) The dynamic viscosity *m* = 0.001 kg/m×s;

You are required to carry out the following CFD analysis using the CFD code ANSYS Fluent 18.2 with the mesh generation using ANSYS and to self-determine the hot water flow rate to ensure 2300 < *Re _{D}* < 10

^{5}:

- Present, respectively, the velocity, temperature and static pressure distributions and profiles at different downstream locations of the tube;
*(assume wall thickness of 8mm)*

**[25 marks]**

- Discuss the simulation results in detail and your findings;

**[15 marks]**

- Calculate the pressure drop across the spiral groove circular tube using the cross-section area-weighted average static pressure at the inlet and outlet of the tube, which can be obtained from the CFD simulation. Find the Darci friction factor for the spiral groove tube and compare the result with that calculated using the Blasius equation. Find the cross-section area-weighted average temperature at the outlet of the spiral groove tube from the CFD simulation and calculate the average temperature on the wall of the tube, respectively, using the Nusselt number from the CFD and that from equation (4).

**[20 marks]**

** **

You are now required to perform a static structural analysis of the grooved pipe depicted below. The pipe is made of structural steel with both ends clamped.

Tube Outer Diameter: D_{o } = 36 mm

Young’s Modulus: E = 205 GPa

Tensile Yield Stress: s = 370 MPa

Poisson’s Ratio: u = 0.3

Reference Temperature: T_{ref} = 22 ^{o}C

Thermal conductivity l = 16.27 W/(mK)

- Use the temperature distribution calculated in question a.) as an internal boundary condition for a steady state thermal analysis to determine the temperature distribution in the tube material. The outside of the tube is subjected to convection with a heat transfer co-efficient of a =5 W/(m
^{2}K). Ensure your computational grid is suitable.

**[20 marks]**

- Apply the calculated body temperature to conduct a static structural analysis of the grooved pipe. Also include the calculated pressure drop from question a.). Assume an inlet gauge pressure 1 bar. Evaluate the stress distributions and deformations and critically discuss the results.

**[20 marks]**

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