University:
Boston University
Course:
CAS PY 211 | General Physics I
Academic year:

2020
Views:

220

Pages:

17
Author:

Giselle A.

Natural Convec.on-‐Driven Propulsion Overview • Experimental data taken from Mercier, et al. (2014) “Self-‐ Propulsion of Immersed Objects via Natural Convec;on.” Physical Review LeXers 12:204501 • The system is analy.cally complicated, requiring coupled governing equa.ons for both ﬂuids and heat transfer • Our goal is to construct a faithful simula.on using OpenFOAM CFD so_ware, as well as an accurate but tractable model that we can use to approximate the experimental and numerical results Experiment Experimental setup, le_, and experimentally measured velocity proﬁle near heated edge, right. Figures taken from Mercier, et al. Developing the Analy.cal Model • Begin with essen.al correla.ons • Correlate drag force with thermal expansion Nusselt Condi-on Correla-on Deﬁni-on (1) Forced Convec-on: laminar ﬂow over a ﬂat plate (2) Natural Convec-on: heated bo=om of an inclined wall (3) Cons-tuent Terms • Resultant Nu for convec.on-‐ driven ﬂow over a body Extension of Natural Convec-on to Velocity Drag Force Pressure Gradient Hydrosta-c Pressure Thermal Expansion (4) (5) (7) (8) (12) Natural convec-on velocity correla-on Comparing Nu Formula.ons Temperature-‐Velocity Correla.on for several Nu formula.ons • Adding the forced convec.on rela.on, we arrive at an upper bound for T and v • The forced correla.on only accounts for forced velocity; the actual velocity includes free convec.on and so should be larger • Therefore the T es.mate is an upper bound Analy-c Model Results Natural Convec-on Forced Convec-on Experimental 32.42 5.0 Modeling Heat Transfer GOVERNING EQUATIONS • SIMULATED VELOCITY Meshing • Modeled a sta.onary wedge with ﬂuid moving around it • Block Mesh • Divided Region into seven blocks • Finer Meshes around the wedge FINAL MESH Solvers BUOYANT SIMPLE FOAM • Steady State: no dt term • Added relaxa.on factor to help converge • Reduces the amount p can change over itera.ons • Polynomial ﬁt of thermal proper.es • Another op.on is a Boussineq model with β constant PRESSURE • Pressure ﬂux model Solves for pressure without gravita.onal inﬂuence • Allows constant boundary condi.on on ver.cel walls • • Used a Gauss Siedel solver for pressure • Can solve both symmetric and asymmetric matricies Boundary Condi.ons • Approxima.ons that need to ﬁt the data • Temperature: • Zero Gradient • Inlet: Constant velocity • Variable Pressure (constant ﬂux) • • Outlet: inletOutlet Condi.on • Free movement of ﬂuid, with average velocity • Constant pressure • • Surface: 0 total velocity • Free movement of ﬂuid • Constant pressure • Velocity Proﬁle near Heated Wall 5.00E-‐07 4.00E-‐07 40200 |U| 3.00E-‐07 30200 21600 14400 8600 2.00E-‐07 4200 1.00E-‐07 0.00E+00 0 0.02 0.04 0.06 0.08 Posi.on on Wall 0.1 0.12 0.14 0.16 0 -‐1.00 Posi.on on Wall 0.148567 0.145535 0.142503 0.139471 0.136439 0.133407 0.130375 0.127343 0.124311 0.121279 0.118247 0.115215 0.112183 0.109151 0.10612 0.103088 0.100056 0.0970236 0.0939916 0.0909596 0.0879276 0.0848956 0.0818636 0.0788316 0.0757997 0.0727677 0.0697357 0.0667037 0.0636717 0.0606397 0.0576077 0.0545757 0.0515438 0.0485118 0.0454798 0.0424478 0.0394158 0.0363838 0.0333518 0.0303199 0.0272879 0.0242559 0.0212239 0.0181919 0.0151599 0.0121279 0.00909596 0.00606397 0.00303199 % Change % Change in Velocity Near Heated Wall 399.00 349.00 299.00 249.00 199.00 8600 14400 149.00 21600 30200 40200 99.00 49.00 0 Posi.on on Wall 0.148567 0.145535 0.142503 0.139471 0.136439 0.133407 0.130375 0.127343 0.124311 0.121279 0.118247 0.115215 0.112183 0.109151 0.10612 0.103088 0.100056 0.0970236 0.0939916 0.0909596 0.0879276 0.0848956 0.0818636 0.0788316 0.0757997 0.0727677 0.0697357 0.0667037 0.0636717 0.0606397 0.0576077 0.0545757 0.0515438 0.0485118 0.0454798 0.0424478 0.0394158 0.0363838 0.0333518 0.0303199 0.0272879 0.0242559 0.0212239 0.0181919 0.0151599 0.0121279 0.00909596 0.00606397 0.00303199 % Change % Change in Velocity (Detail) 60.00 50.00 40.00 30.00 8600 14400 21600 30200 20.00 40200 10.00 0.00 Average %Change vs Mesh Size 30.00 8,600; 26 25.00 Average % Change 20.00 14,400; 16 15.00 21,600; 13 30,200; 13 40,200; 9 10.00 5.00 0.00 0 5000 10000 15000 20000 25000 # Cells 30000 35000 40000 45000 Wedge Velocity vs Temperature Wedge Velocity with Temperature 0.000589 0.000588 0.000587 0.000586 0.000585 0.000584 0.000583 0.000582 296 298 300 302 304 306 308 310 312 314 0 0.00303199 0.00606397 0.00909596 0.0121279 0.0151599 0.0181919 0.0212239 0.0242559 0.0272879 0.0303199 0.0333518 0.0363838 0.0394158 0.0424478 0.0454798 0.0485118 0.0515438 0.0545757 0.0576077 0.0606397 0.0636717 0.0667037 0.0697357 0.0727677 0.0757997 0.0788316 0.0818636 0.0848956 0.0879276 0.0909596 0.0939916 0.0970236 0.100056 0.103088 0.10612 0.109151 0.112183 0.115215 0.118247 0.121279 0.124311 0.127343 0.130375 0.133407 0.136439 0.139471 0.142503 0.145535 0.148567 Temperature along Hot Edge 298 297 296 295 294 Temperature at 0.1mm Temperature at 0.2mm 293 292 291 Heat Flux: 4200-‐6300W Plate Temperature: 297K Velocity Proﬁle Discussion and Future Work • The concept works and the numerical data matches • Lessons learned: Relaxa.on factors are good for eﬃciency, but don’t help un.l the code works • Be willing to try many boundary condi.ons, even if they seem unlikely to work • Finer meshes don’t always work • • Future work: Write in a shell code for itera.ve process • Try diﬀerent shapes, temperature and heat ﬂuxes •