Ansys Natural Convection flow powerpoint
- 1. Intro to Natural Convection Natural Convection – Lesson 1 • DECEMBER 2019
- 2. 2 Intro • Convection heat transfer resulting from an external forcing condition such as that induced by a fan (or a pump) is known as forced convection. • In situations where there is no external forcing condition, convection heat transfer may still occur due to the convection currents that exist within the fluid owing to density gradients. This is referred to as free or natural convection. • Natural convection occurs due to a buoyancy force that acts on a fluid having density gradients. The density gradients can be due to a temperature gradient. • The flow velocities are generally smaller than those associated with forced convection and therefore the corresponding convection heat transfer rates are also smaller. • As a result, applications relying on natural convection are typically larger in size compared to their forced convection counterparts. Natural Draft Cooling Tower – Natural Convection Forced Draft Cooling Tower – Forced Convection
- 3. 3 Applications of Natural Convection • Natural convection plays an important role in many industrial applications such as power generation, food processing, electronics cooling, etc. • Moreover, it is the driving force of many natural processes such as ocean and atmospheric currents. Natural Draft Cooling Tower Electronics cooling HVAC Ocean Currents
- 4. 4 Applications of Natural Convection (cont.) • Buoyancy-induced flow in a fluid is driven by an external body force when density gradients arise due to temperature differences. • The body force is gravitational in most of the cases; however, it can be the centrifugal force in rotating machinery or the Coriolis force in the case of oceanic and atmospheric currents. • The density of fluids depends on temperature and it generally decreases with increasing temperature. This is because as the temperature increases, the fluid expands and its volume increases. • In this course we will focus on natural, or free, convection in which the density gradient is due to a temperature gradient and the body force is gravitational.
- 5. 5 Physics of Natural Convection • As an example of natural convection, let’s consider a fluid enclosed by two large horizontal plates where the lower plate is at a higher temperature than the upper plate. • As a result, the density decreases in the direction of the gravitational force. • If the temperature difference is such that the buoyancy forces can overcome the viscous forces, then the designated fluid circulation would be set up. • The heavier fluid will descend, being warmed in the process, while the lighter fluid will rise and cool as it moves. • On the other hand, if the temperature of the upper plate is higher, then the fluid density will not decrease in the direction of gravity and the flow pattern described above will not set up. In this case, heat will be transferred via conduction. Unstable fluid circulation 𝑇𝐴 𝑇𝐵 𝜌𝐴 𝜌𝐵 𝑔 𝑥 𝑑𝑇 𝑑𝑥 > 0 𝑑𝜌 𝑑𝑥 < 0 Stable 𝑇𝐴 𝑇𝐵 𝜌𝐴 𝜌𝐵 𝑔 𝑥 𝑑𝑇 𝑑𝑥 < 0 𝑑𝜌 𝑑𝑥 > 0 Unstable temperature gradient in fluid between large horizontal plates at different temperatures Stable temperature gradient in fluid between large horizontal plates at different temperatures
- 6. 6 Unbounded Natural Convection • Unbounded buoyancy-driven flows are formed in the absence of a bounding surface. • Two common examples are plume formation over an immersed heated object and a buoyant jet from a heated discharge in a cooler fluid. • A plume is formed from the fluid rising from a heated object submerged in a quiescent fluid. • The hot fluid rises due to buoyancy forces and entrains more fluid from the quiescent region. One example is a plume formed from a hot immersion water heater. • The width of the plume increases with distance from the heated object, however, the plume itself eventually dissipates due to viscous effects and reduction in the buoyancy forces. Plume formation over a heated wire 𝑥 𝑦 Plume 𝑇∞ 𝑢∞ = 0 𝜌∞ 𝑔
- 7. 7 Unbounded Natural Convection (cont.) Buoyant jet from a heated discharge 𝑇∞ 𝑢∞ = 0 𝜌∞ 𝑔 • Unlike plumes, buoyant jets have some initial velocity as shown. • They arise when a heated fluid is discharged as a jet into a quiescent medium of lower temperature. • Due to the buoyant forces, the jet gains an additional vertical velocity component. • For example, consider the situation when warm water from the condenser of a power plant is discharged into a reservoir of cooler water.
- 8. 8 Bounded Natural Convection • In this course we will focus on natural convection flows that are bounded by a surface. • A canonical example of such flows is the boundary layer developed on a heated vertical plate. • The plate is fully immersed in an extensive quiescent fluid having 𝑇𝑠 > 𝑇∞. As a result, the fluid close to the plate is warmer compared to the fluid that is farther away from the plate. • As a result, the fluid close to the plate is less dense and the buoyancy forces induce a natural convection boundary layer in which the heated fluid rises vertically, entraining fluid from the quiescent region. • The resulting boundary layer is different from the one we get in the case of forced convection. • The velocity is zero as 𝑦 → ∞, as well as at 𝑦 = 0. • A natural convection boundary layer will also develop if 𝑇𝑠 < 𝑇∞; however, the fluid motion in this case will be downwards. Boundary layer development on a hot plate immersed in a cooler fluid 𝑇𝑠 𝑥 𝑢 = 0 𝑢 = 0 𝑇∞ 𝑇𝑠 𝑦 𝑇(𝑦) u(𝑦) 𝑔 Stationary Fluid
- 9. 9 Governing Equations of Natural Convection • Consider the laminar boundary layer flow shown in the previous slide. • Assuming steady, 2D, constant property conditions where gravity acts in the negative x-direction and the boundary layer approximations are valid, the x-momentum equation can then be written as: • Here 𝑑𝑝∞/𝑑𝑥 is the free stream pressure gradient outside the boundary layer, where 𝑢 = 0; thus the above equation reduces to 𝑢 𝜕𝑢 𝜕𝑥 + 𝑣 𝜕𝑢 𝜕𝑦 = − 1 𝜌 𝑑𝑝∞ 𝑑𝑥 − 𝑔 + 𝜈 𝜕2 𝑢 𝜕𝑦2 𝑑𝑝∞ 𝑑𝑥 = −𝜌∞𝑔
- 10. 10 Governing Equations of Natural Convection • Substituting this in the x-momentum equation, we get the following: • 𝑔(Δ𝜌/𝜌) represents the buoyancy force. If the density variations are only due to temperature variations, then this term can be related to the volumetric thermal expansion coefficient: • The volumetric thermal expansion coefficient is a measure of the amount by which the density changes in response to a change in temperature at constant pressure. 𝑢 𝜕𝑢 𝜕𝑥 + 𝑣 𝜕𝑢 𝜕𝑦 = 𝑔(Δ𝜌/𝜌) + 𝜈 𝜕2𝑢 𝜕𝑦2 where Δ𝜌 = 𝜌∞ − 𝜌 𝛽 = − 1 𝜌 𝜕𝜌 𝜕𝑇 𝑝
- 11. 11 Boussinesq Approximation • The volumetric thermal expansion coefficient can be approximated using the following equation: • This simplification is known as the Boussinesq Approximation. Substituting this in the momentum equation we obtain the following equation for the x-momentum: • The expansion coefficient 𝛽 can be determined for ideal gases (𝜌 = 𝑝/𝑅𝑇) using the following relation: • Here 𝑇 is the absolute temperature. In the case of liquids and non-ideal gases, 𝛽 is obtained from property tables. 𝑢 𝜕𝑢 𝜕𝑥 + 𝑣 𝜕𝑢 𝜕𝑦 = 𝑔𝛽(𝑇 − 𝑇∞) + 𝜈 𝜕2𝑢 𝜕𝑦2 𝛽 ≈ − 1 𝜌 Δ𝜌 Δ𝑇 = − 1 𝜌 𝜌∞ − 𝜌 𝑇∞ − 𝑇 𝜌∞ − 𝜌 ≈ 𝜌𝛽(𝑇 − 𝑇∞) 𝛽 = − 1 𝜌 𝜕𝜌 𝜕𝑇 𝑝 = 1 𝜌 𝑝 𝑅𝑇2 = 1 𝑇
- 12. 12 Governing Equations of Natural Convection • Since the buoyancy effects are confined to the momentum equation, the mass and energy conservation equations are similar to forced convection: • However, unlike forced convection, the solution to the momentum equation now depends on the knowledge of 𝑇 and hence on the solution of the energy equation. • Thus, the above-mentioned governing equations are strongly coupled and must be solved simultaneously. 𝑢 𝜕𝑢 𝜕𝑥 + 𝑣 𝜕𝑢 𝜕𝑦 = 𝑔𝛽(𝑇 − 𝑇∞) + 𝜈 𝜕2𝑢 𝜕𝑦2 𝜕𝑢 𝜕𝑥 + 𝜕𝑣 𝜕𝑦 = 0 𝑢 𝜕𝑇 𝜕𝑥 + 𝑣 𝜕𝑇 𝜕𝑦 = 𝛼 𝜕2𝑇 𝜕𝑦2 Mass: Momentum: Energy:
- 13. 13 Summary • In this lesson, we introduced the concept of natural (or free) convection and explained how it is different from forced convection. • We discussed some of the applications of natural convection and understood its underlying physics. • Bounded and unbounded natural convection flows were also discussed. • Lastly, we derived the governing equations of natural convection.