Week 1- Mixing Tee

Provide Aim, introduction, and theory of the topic and its importance in practical applications.

Aim: To perform the steady flow simulation of Tee joints of different lengths (called to be short tee and long tee) for the mixing of two stream lines of fluid at different temperatures. 

Introduction: In this challenge we have to simulate the two streams of fluid (air)mixing each other at different temperatures across the tee joints. The tee joint is a joint in which two fluids are mixing in a transverse direction to each other. For example, In household piping if we want to distribute the water in various taps of kitchen or washrooms then we have to introduce a tee joints corresponding to those taps from the main pipe line. In Industries if we require a mixing of two fluids or maintaing the temperature of hot/cold fluids then we can intrduce the hot/cold fluid to the main streamline through the tee joint. 

Theory of the toipic: Here in this case we are silulating the two cases for tee joints of different lengths along with the different stream velocities. In these case, we have a short tee and long tee with two momentum ratios 2,4 for the fluid flow. Momentum ratio is a ratio between cold fluid velocity to the hot fluid velocity. Here the main stream fluid is hotter and cold fluid is introduced to main stream thruogh the tee joint. We are simulating for the perdiction of final average temperature of the fluid after mixing, mixing efficiency and to study the effect of change in momentum and geometry of the tee joints on mixing two fluids.

Importance in Practical Applications:

1. Mixing of cold air to the hotter room atmosphere for air conditioning in homes. hotels and offices.

2. mixing of cryogenic fluids in industrial applications.

3. Mixinf of fresh air in ICU ventilation in hospitals. 

Analytical Method: 

Case 1: Short Tee with momentum ratio 2

          Given:  Temperature of hot stream, Tc= 36 C

                      Temperature of cold stream,Th = 19 C

                      Velocity of hot stream, Vh = 3m/sec

                     Momentum ratio= 2  {i.e. ratio of cold fluid to hot fluid velocity}

                     therefore, velocity of cold fluid,Vc= 3x2= 6m/sec

   From mass balance equation,

                    mass flow rate of hot stream + mass flow rate of cold stream = mass flow rate of outer stream

                    mass flow rate = density of fluid x cross section area  x Velocity of fluid stream 

        From balancing mass balance equation,

         Velocity of fliud at the outlet, Vo = Vh+(Dc/Do)2 x Vc 

Also, From Energy balance equation,

Energy of cold stream+Energy of hot stream = Energy of the outer stream

Ec + Eh = Eo

Energy= mass flow rate x Enthalpy

From here, To = {(mc)'Tc + (mh)'Th}/(mo)'  , where (mx)' represents mass flow rate of x stream

Case 1: Short Tee with momentum ratio = 2

Therfore, Vc = 6m/s

               Vh = 3m/s   

Case 2: Short Tee with momentum ratio = 4

Therfore, Vc = 12 m/s

              Vh = 3m/s

Case 3: Long Tee with momentum ratio =2

therefore, Vh = 3m/s

                Vc = 6m/s                                     

 Case 4: Long Tee with momentum ratio = 4

therfore, Vh = 3m/s

              Vc = 12m/s

From Space Claim, We have

Dh = 33.9mm

Ah = 901.3138 mm2

Dc = 16.963mm

Ac = 225.982 mm2

Length of Short Tee = 192.38mm

Length of Long Tee = ?? mm