Numerical simulation of the effects of the vortex generator on increasing the heat transfer of non-Newtonian fluids in a square channel

Dissertation

To receive a master's degree

Abstract

Achieving higher rates of heat transfer using different techniques that can result in significant energy savings and also lead to the production of devices To be more compact and cheaper with higher thermal efficiency has been the focus of researchers. Vortex generation is one of the best methods used to increase heat transfer. In recent years, due to the widespread use of non-Newtonian fluids in chemistry, pharmaceutical, petrochemical, food and electronic industries, this group of fluids has attracted special attention. Considering the importance of non-Newtonian fluids in the industry, and in order to increase efficiency in increasing heat transfer, this study has been done for non-Newtonian fluids.

In the present research, first, the structure of flow and heat transfer from two back-to-back square cylinders exposed to a non-Newtonian fluid with the Powerlaw model in two dimensions, and then the behavior of flow and heat transfer from a pair of vortex generators in a square channel in three dimensions and using the volume method limited and the SIMPLEC algorithm has been studied numerically. In this research, incompressible and laminar non-Newtonian fluid flow in the Reynolds number range of 500 Re 50 has been investigated. The Prantel number is considered equal to 50. Also, the effect of Powerla's index on the behavior of flow and heat transfer in the range of 1.8 to 0.6 has been investigated. In this research, in two-dimensional mode, the effect of the angle of deviation of cylinders from the main flow and the distance between cylinders, and in three-dimensional mode, the effect of the height of vortex generators on flow behavior and heat transfer were investigated. The results obtained in two-dimensional mode include drag and lift coefficients, pressure coefficient and Nusselt number on the faces of the cylinders. In the three-dimensional mode, the pressure and friction coefficients on the channel walls, bulk temperature ( ), Colburn factor, Nusselt number and finally the JF parameter were obtained as the thermal performance coefficient as a scale for the channel performance with and without the vortex generator.

The results of the two-dimensional problem showed that by increasing the Powerlaw index and decreasing the angle of deviation of the cylinders, as well as decreasing the distance between the cylinders, the Strouhal number decreased. finds By reducing the Powerlaw index and by increasing the inter-cylinder distance, the total Nusselt number increases on the faces of both cylinders. Also, in the three-dimensional mode, it was concluded that pseudo-plastic fluids act more effectively than other fluids in increasing the overall performance coefficient of the channel. Also, reducing the height of the vortex generator increases the overall performance of the channel.

Chapter One

Introduction

1-1 Boundary layer

The hydrodynamic boundary layer is a region of the flow where the shear stress forces are the forces caused by the presence of the solid wall. or the area where the surrounding flow is affected by the presence of the wall. In other words, the hydrodynamic boundary layer is a region of the flow where the fluid feels the friction and drag [1] resulting from the presence of the wall. In this case, the molecules closest to the wall (which are attached to the wall) do not move at all relative to the wall due to the no-slip condition. By moving away from the wall, the effect of the wall on the flow decreases so much that the flow no longer feels the presence of the wall, or in other words, the effect of the wall on the layers around the flow disappears. This area far enough from the wall and unaffected by the wall is called the free flow area. From the point of view of heat transfer, the thermal boundary layer (Figure 1-2) is an area where, from the point of view of temperature distribution, the surrounding flow is affected by the presence of a wall with a different temperature than the flow. The formation of the thermal boundary layer and the layering of the fluid causes the formation of insulation and the formation of resistance against heat transfer from the wall to the fluid. In the boundary layer formed in turbulent flows, due to the turbulent movements of the flow, the regular shape of the flow layers adjacent to the wall is lost, and therefore the barrier layers between the wall and the free flow are removed in a way, and better heat transfer takes place compared to smooth flows.

-2 Converting smooth to turbulent flow

In order to reach turbulent flow, especially on solid surfaces and inside open channels or pipes, the flow must first enter the transition stage from smooth to turbulent and finally enter the turbulent flow phase. Sometimes, due to various external factors, the transient area may shrink or even disappear, in which case we will witness the direct transformation of the smooth flow into turbulent flow along a short path. For example, in the boundary layer formed on non-smooth surfaces or on surfaces with mass transfer through surfaces or in mixed flows or in supersonic flows where we have the interaction of shock and boundary layer, we can see situations in which we can witness the transformation of smooth to turbulent flow within a very short distance. Local nuclei and seeds of turbulence pile up so much that they fill the entire flow field. This process can be considered as the gradual pollution of a stream passing over a polluted surface, in short intervals and times, a major part of the stream is clean and only a small part of it is polluted, but if this process is given enough time and space and there is no agent to remove the pollution, so much pollution accumulates in the stream that the entire stream becomes polluted. This gradual process of accumulation of local masses of turbulence is called the process of passing from the state of smooth to turbulent flow. To pass from the state of calm to turbulent flow, a certain distance and time are needed so that the entire flow is saturated with nuclei of turbulence.

As the amount of turbulence in the free flow increases or the surface roughness increases, we can expect that the transition from calm to turbulent state will occur in a shorter distance and in other words faster, and vice versa. The amount of disturbance in the free flow can be considered as the seeds of disturbance in the free flow, if these seeds are placed in a favorable space for growth and development, they can cause the flow to be disturbed. It does not matter how these seeds were created or from which source they originated. In some other engineering problems, effects such as centrifugal effect, density change effect, gravity effect and cavitation effects, bubble bursting, chemical reactions, electromagnetic field disturbance effects, etc. can also accelerate the flow to reach a turbulent state. [1]

1-3 flow separation

Two very important effects in fluid flow include the effects of inertia and viscosity. The degree of mutual influence of these two effects is evaluated by defining the dimensionless Reynolds number. This number is defined as the ratio of inertial forces to viscous forces: (1-1) A large Reynolds number means that inertial effects are dominant and a small one means that viscous effects are dominant. It should be noted that the concept of Reynolds number in relation to the boundaries that affect the flow is a local quantity. In other words, different choices of the characteristic length L in the calculation of the Reynolds number will lead to different values ??for this parameter. Therefore, the flow over a body may include a wide range of Reynolds numbers depending on the location of the study. Therefore, in the discussion of the flow that passes over an object, the characteristic length L is usually chosen in such a way that it represents a general dimension of the object. Basically, viscosity tends to stop the movement of the fluid, and if there is no factor to continue the flow, the movement of the fluid gradually decreases due to the presence of viscosity and eventually stops. The factor that keeps the flow in the boundary layer is the pressure gradient. The negative pressure gradient in the direction of the flow is the factor of strengthening the flow and increases the momentum of the fluid, in this case, the thickness of the boundary layer tends to decrease, but if the pressure increases in the direction of the flow (reverse pressure gradient), the thickness of the boundary layer increases rapidly.