inflow outflow Part I. Regular tasks for MAE598/494 Task 1

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1 MAE 494/598, Fall 2016 Project #1 (Regular tasks = 20 points) Har copy of report is ue at the start of class on the ue ate. The rules on collaboration will be release separately. Please always follow the rules. Part I. Regular tasks for MAE598/494 Task 1 A simple hot water tank, illustrate in Figs. 1-3, consists of a main cylinrical tank an two small sie pipes for the inlet an outlet. All soli surfaces of the system are thermally insulate, except that the temperature at the bottom of the main cyliner is externally maintaine at a constant 65 C. For this exercise, the temperature of the water entering the inlet is set to 25 C. As cool water flows through the tank, it is heate up by the hot plate at the bottom. Thus, at the steay state we expect the temperature of the outflow to excee 25 C. Using Ansys-Fluent, the main objective of this task is to analyze how the steay-state temperature of the outflow is affecte by the vertical positions of the inlet an outlet. Use the same setup for material an bounary conitions as Tutorial #1, except the following: (1) Turn "gravity" on an set it as the regular gravity, i.e., 9.8 ms 2 in the z-irection. (2) Instea of setting ensity as constant, switch to "Boussinesq" to allow buoyancy-riven thermal convection. With this setup, the operating ensity, operating temperature, an thermal expansion coefficient also nee to be given accoring to the Boussinesq approximation. This etail will be iscusse in class. (3) Choose secon orer iscretization. (See Step 10 of Tutorial #2.) The key geometric parameters are efine in Figs. 2 an 3. For this task, use H = 1.0 m, D = 0.5 m, = 0.04 m, an = 0.1 m. Only the height of the center of the sie pipe (Z 1 for the inlet, Z 2 for the outlet) will be varie. Choose u = 0.05 m/s as the inlet velocity. The velocity an temperature at the inlet are uniform for all cases. inflow outflow Fig. 1 The water tank system which consists of a main cyliner an two circular sie pipes for the inlet an outlet.

2 D inlet outlet Plane of symmetry Fig. 2 Top view of the water tank system with a circular cross section. Key parameters: D is the iameter of the main cyliner; is the iameter of both sie pipes; is the length of both sie pipes. D H Z 1 Z 2 Fig. 3 The vertical cross section of the water tank system along its plane of symmetry. Key parameters: H an D are the height an iameter of the main cyliner; Z 1 an Z 2 are the heights of the centers of the sie pipes for the inlet an outlet, respectively; is the length of both sie pipes; is the iameter of both sie pipes.

3 Choose "turbulence k-epsilon" moel an seek "steay state" solution. Consier the following two esigns with contrasting vertical positions of the sie pipes for inlet an outlet: Case A: Z 1 = 0.8 m, Z 2 = 0.2 m Case B: Z 1 = 0.2 m, Z 2 = 0.8 m (i.e., swapping the vertical positions of inlet an outlet from Case A) Run Ansys-Fluent simulations for the two cases to obtain the temperatures at the outlet. Because the temperature an velocity at the outlet are generally non-uniform (cf. Task 3 of HW1), a more meaningful efinition of the average temperature is T out = v n T A v n A, Eq. (1) where v n is the non-uniform velocity normal to the outlet an T is the non-uniform temperature at the outlet, an the integral is performe over the circular opening of the outlet. Please use this efinition of T out through the entire project. The eliverables for this task are (1) The values of outlet temperature, T out, from the simulations of the two cases. (2) Contour plots of temperature on the plane of symmetry for the two cases. (3) Contour plots of temperature on the horizontal cross sections at Z = 0.2 m an Z = 0.8 m, for the two cases. [Revise: eliverable (3) is no longer require for Task 1-3 an Challenge #1.] (4) Plots of stream lines for the two cases. (An example of acceptable format can be foun in p. 9 of the set of slies name "More slies from the first lecture" poste at our class website. Follow the example in the right panel of that slie that shows the 3-D structure of the stream lines.) (5) A iscussion of the possible reasons for the ifferences in T out between the two cases base on the information obtaine from the numerical simulations. Task 2 This task will assess the epenence of T out on the geometry of the main water tank by consiering two aitional esigns as shown in Fig. 4. In both cases, all esign parameters follow Case B in Task 1 (specifically, Z 1 = 0.2 m, Z 2 = 0.8 m) except that the horizontal cross section of the tank is change from circular to elliptical. By choosing D 1 an D 2 (see Fig. 4) such that D 1 D 2 = D 2 (where D is the iameter of the circular esign in Fig. 2), the total volume of the main tank remains the same as the esign in Task 1. Specifically, consier: Case C: D 1 = m, D 2 = 0.4 m. The inlet an outlet are aligne with the major axis of the ellipse. See upper panel of Fig. 4. Case D: D 1 = 0.4 m, D 2 = m. The inlet an outlet are aligne with the minor axis of the ellipse. See lower panel of Fig. 4. Perform Ansys-Fluent simulations for the two cases an prouce the same eliverables as escribe in Task 1. In eliverable (5), compare the efficiency of the elliptical esign with the circular one in Task 1.

4 D 1 Plane of symmetry D 2 inlet outlet D 1 Plane of symmetry D 2 inlet outlet Fig. 4 The two "elliptical esigns". Top: The inlet an outlet are aligne with the major axis. Bottom: The inlet an outlet are aligne with the minor axis. Not rawn to scale.

5 Task 3 Consier Case A in Task 1 but now set ensity to constant an turn off gravity. Repeat the simulation an prouce the counterparts of eliverables (1)-(5) in Task 1. In eliverable (5), iscuss what critical process(es) are missing when ensity is set to constant, an how they affect the value of T out. Part II. Regular task for MAE598 only Participants of MAE 494 o not nee to complete the task in this part. Work submitte by MAE 494 stuents for this part will not be grae an will not be aware any point. Task 4 (a) Consier Case B in Task 1. In that case, the bounary conition at the bottom of the water tank is "temperature = 65 C". At the steay state, since the temperature in the interior of the tank is generally lower than the impose temperature at the bottom plate, there is a net heat flux into the tank from the bottom plate. Since water oes not flow through the bottom plate, this heat flux is ue to heat conuction. Using ieas similar to those consiere in Task 3 of Homework 1, evaluate the total flow rate of heat from the bottom plate into the tank. (As is in Task 3 of HW1, this quantity shoul have the unit of Watts.) (b) Divie the total flow rate of heat, as etermine from (a), by the area of the bottom plate to obtain the average heat flux at the bottom plate. Repeat the simulation of Case B in Task 1 by replacing the "constant temperature" ("temperature = 65 C") bounary conition at bottom plate with that of an impose constant heat flux, using the value of the average heat flux etermine earlier in this task. Does this simulation prouce the same value of T out as the original simulation for Case B in Task 1? Provie a brief interpretation of your fining.

6 Part III "Bonus pool" challenges Please submit the (har copy) answer to each challenge SEPARATEY, one challenge per report. Do not mix ifferent challenges or mix the challenges with regular tasks. Each correct (or nearly correct) answer earns one share of the bonus. Occasionally, a "half correct" answer might be grante a half share. ow quality answers will receive no creit at all. The actual point(s) earne per share will be the total bonus points for a challenge ivie by the number of shares grante for that challenge. The only exception is if the "points per share" excees a preset cap of rewar. For example, Challenge #1 has 80 points in the pool an a cap of 4 points. If 40 shares are grante, each will be equivalent to 2 points. If only 15 shares are grante, each will be equivalent to 4 points, i.e., the preset cap. The maximum an iniviual can earn from the challenges is 15 points for the semester. Solutions to challenges submitte by an iniviual who alreay has 15 points from the bonus pools will not be grae an will not be aware any point. The rules on collaboration for challenges are the same as those for regular tasks, except that (i) No nee to use the "cover sheet" for submissions of challenges; (ii) No nee to state the etail of collaboration an percentage contribution. Instea, simply inclue a one-line statement of "No collaboration" or "Collaboration with [name of collaborator]" in the first page of the report. Challenge #1 (80 points in the pool; cap = 4 points) In Case B of Task 1, a uniform temperature of 65 C is impose at the bottom plate. Consier a moification of the esign in which non-uniform (but still time-inepenent) temperature is impose at the bottom plate. The impose temperature is axially symmetric, i.e., T T(r) where r is the raial istance from the center of the bottom plate. Specifically, T(r) in C is given as T(r) = 65 exp( r/d), Eq. (2) where D = 0.5 m. [Thus, the impose T is 65 C at the center of the circular plate but rops to 65 exp( 0.5) 39.4 C at the ege of the plate.] Use User Define Function (UDF) to impose the nonuniform temperature, given by Eq. (2), at the bottom plate an repeat the simulation of Case B in Task 1. Prouce the counterparts of eliverables (1)-(4) as escribe in Task 1. In aition, to emonstrate that the setup of the new bounary conition is correct, the following eliverables are also require: (5) The printout of the coe for the UDF (6) Contour plot of temperature on the horizontal cross section at Z = 0 (i.e., at the bottom of the main tank). Challenge #2 (80 points in the pool; cap = 4 points) Using the esign of Case A in Task 1, we wish to etermine the epenence of temperature at ifferent parts of the system on the flow velocity at the inlet, V in. Specifically, we wish to obtain the values of two quantities, T out an T mi, from 10 simulations with V in = 0.01, 0.02, 0.03,..., 0.09, 0.1 m/s. Here, T out is efine by Eq. (1) as in Task 1, with the integration performe over the surface of the outlet.

7 T mi is also similarly efine by the right han sie of Eq. (1) but with the integration performe over the horizontal cross section at Z = 0.5 m (i.e., the circular cross section that cuts through the mile of the tank). While this task coul be accomplishe by manually changing V in repeately an executing 10 separate simulations, Ansys-Fluent has a special tool calle Parametric Design which can be use to set up an automatically execute the 10 simulations in sequence. This challenge requires that you use Parametric Design to complete the 10 simulations. The eliverables are (1) A escription, incluing screenshot(s) of critical step(s), of the setup for parametric esign. This escription shoul also inclue the etail of how the values of T out an T mi are extracte from the 10 runs uner the framework of parametric esign. (2) ine plots of T out an T mi as a function V in. These plots summarize the outcome of the 10 runs. Creit will be given only to the submissions that use parametric esign to complete the task. No point will be aware if eliverable (1) is missing or incorrect, even if correct plots are provie for eliverable (2). In other wors, no point will be aware if the plots in (2) are generate by manually executing 10 separate runs then stitching the results together.