# Preliminary Experimental Study on Pressure Loss Coefficients of Exhaust Manifold Junction

Authors: Xiao-lu Lu; Kun Zhang; Wen-hui Wang; Shao-ming Wang; Kang-yao Deng
Journal: International Journal of Rotating Machinery
 (2014)

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## Abstract

The flow characteristic of exhaust system has an important impact on inlet boundary of the turbine. In this paper, high speed flow in a diesel exhaust manifold junction was tested and simulated. The pressure loss coefficient of the junction flow was analyzed. The steady experimental results indicated that both of static pressure loss coefficientsL13 and L23 first increased and then decreased with the increase of mass flow ratio of lateral branch and public manifold. The total pressure loss coefficient K13 always increased with the increase of mass flow ratio of junctions 1 and 3. The total pressure loss coefficient K23 first increased and then decreased with the increase of mass flow ratio of junctions 2 and 3. These pressure loss coefficients of the exhaust pipe junctions can be used in exhaust flow and turbine inlet boundary conditions analysis. In addition, simulating calculation was conducted to analyze the effect of branch angle on total pressure loss coefficient. According to the calculation results, total pressure loss coefficient was almost the same at low mass flow rate of branch manifold 1 but increased with lateral branch angle at high mass flow rate of branch manifold 1.


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## Body

## 1. Introduction

A very substantial part of the design of a turbocharging system is the exhaust pipe construction. This is because the flow characteristic of the exhaust system has an important impact on the inlet boundary of the turbine, which affects the power out of the turbine. The principle means to understand that the flow characteristics are the numerical simulation. By using a numerical simulation, it is possible to understand the exhaust pipe pressure wave forms and their propagation characteristics and analyze the use of the exhaust energy and cylinder scavenging as well as design and optimization of the exhaust system. In an exhaust system, the pipe is generally a one-dimensional pipe, so a one-dimensional flow analysis can be used. However, there are three-dimensional flows in the exhaust manifold junction of the exhaust pipe system; so, using a one-dimensional numerical simulation will result in a large error. Accuracy in the pressure loss coefficient simulation of the exhaust manifold junction of the exhaust pipe system is essential. During the existing one-dimensional simulation of the engine, when the exhaust gas passes with a higher flow rate, the accuracy of the calculated pressure loss of the tee is relatively low.In papers [1–6], several researchers have studied the pressure loss coefficient of the exhaust manifold junction. The research showed that the pressure loss coefficient is mainly affected by the flow ratio between the public manifold and branch manifold and that 12 circulation types of the pressure loss coefficient calculation formula are deductible. However, during the theoretical derivation process, the junction fluid is assumed to be an incompressible fluid. When the public manifold Mach number is greater than 0.2, the pressure loss coefficients between the calculated and experimental were quite different. In papers [7–9], some experimental research on the pressure loss model of the exhaust manifold junction of the “T” type was done. The research showed that the pressure loss coefficient was related not only to the flow ratio between the public manifold and branch manifold but also to the Mach number in the public manifold. However, during the experiment, the diameter of the branch manifold was only 12 mm, which was much smaller than that in a real engine, and the flow type of the junction was not common in exhaust manifold.In this paper, the high speed flow in a diesel exhaust manifold junction was measured. The pressure loss coefficients of the exhaust manifold junction with high speed flow were analyzed. The results provide reference for the pressure loss junction model considering gas compressibility. At last, the internal flow phenomena of junction were analyzed by CFD model, and the effect of branch angle on total pressure loss coefficient was also studied.


## 2. Materials and Experiment

A schematic diagram of the experiment is shown in Figure1. A 400 kW step motor was used to drive the compressor, and the bleed valve was installed behind the compressor to prevent the compressor from surging during the test. The pressure sensor 2, Pitot tube, and temperature sensor 4 were installed in the public manifold that comes after the compressor. Pressure sensor 3 was installed behind the Pitot tube to measure the difference between the total pressure and static pressure. Flow control valves 1 and 2 were the gate valves, and schematic diagram is shown in Figure 2. The flow within the pipe was changed by lifting the valve. A mass flow sensor that could measure range ratio of 1000 : 1 was installed after flow control valve 2 to measure the mass flow of the gas in branch manifold 2. Temperature sensors were installed in the manifold branches 1 to 3 to measure the gas temperature. Pressure sensor 2 was installed in the branch manifold to measure the pressure. Differential pressure transducer 1 was installed to measure the pressure difference between branch manifold 1 and branch manifold 3. Differential pressure transducer 2 was installed to measure the pressure difference between branch manifold 2 and branch manifold 3. To regulate the back pressure in branch manifold 3, a back pressure valve was installed after branch manifold 3.Figure 1
Schematic diagram of the experiment.Figure 2
Schematic diagram of the valve.A photograph of the junction is shown in Figure3. The junction was made by stainless steel to reduce the wall friction loss. The diameter of the three branch manifolds was 66 mm, which is equal to the diameter of the pulse turbocharging system of a heavy duty vehicular diesel engine. The angle between branch manifold 1 and 2 was 45°. The point A was the intersection point of the center lines. The distances between point A and measuring point 1, between point A and measuring point 2, and between point A and measuring point 3 were 260 mm, which was equal to 4 times of the pipe diameter. The lengths of branch manifold 1, branch manifold 2, and branch manifold 3 were all 0.65 m.Figure 3
Photograph of the junction.Measurement ranges of every sensor are shown in Table1. The output signals of the 10 sensors are the voltage signal, which were collected by a MP426 high-speed data acquisition card. The sampling frequency of the MP426 was 1 KHz.Table 1
Details of main sensor.
Sensor
Model number
Measuring range
Measurement method
Measuring accuracy
Mass flow sensor
GFM200
0–8000 m3/h (Air standard conditions)
Vortex-shedding flowmeter
±1%
Pressure sensors 1 and 2
NS-I7
0–300 kPa (Gage pressure)
Piezoresistive pressure transducer
±0.5%
Temperature sensors 1, 2, 3, and 4
PT100
0–650°C
Thermocouple temperature sensor
±0.15%
Differential pressure sensors 1 and 2
NS-1151DP
0–50 kPa
Capacitive differential pressure sensors
±0.5%
Differential pressure sensor 3
NS-1151DP
0–30 kPa
Capacitive differential pressure sensors
±0.5%The diameters of the public manifold, flow control valve 1, and flow control valve 2 were 150 mm. The mass flow sensor was installed in a pipe that was 200 mm in diameter and 2.6 m in length. The larger diameter was used to meet the flow measurement range of the compressor, while the measurement accuracy was guaranteed by the long straight pipeline.


## 3. Test Procedure and Data Processing Method

### 3.1. Test Procedure

In the test, in order to prevent a compressor from surging, the purge valve was only opened 30%. By using a step motor, the compressor worked at three speeds: 9000 r/min, 12000 r/min, and 15000 r/min.At each compressor speed, the flow control valve 1 was fully closed first, while flow control valve 2 was fully opened. Then, the flow control valve 1 was gradually opened, while flow control valve 2 was kept fully opened, Finally, while keeping flow control valve 1 fully opened, close flow control valve 2 gradually from fully opened to fully closed. The valve lift for each test was 5 mm when the flow control valves were either opened or closed. In each of the situations, output signals from the 10 sensors were collected after the data was stable.


### 3.2. Data Processing Method

Firstly, using the data from pressure sensor 2, temperature sensor 4, and differential pressure sensor 3, calculate the mass flow of the public manifold. Then, using the data from the mass flow sensor under the experimental condition of flow control valve 1 fully closed and flow control valve 2 fully opened, correct the calculated mass flow of the public manifold.The mass flow of branch manifold 3m3 was obtained from correcting the mass flow of the public manifold. The mass flow of branch manifold 2 m2 was obtained from the mass flow sensor. The mass flow of branch manifold 1 m1 was obtained from m3-m2. The static pressure of branch manifold 1 P1 was measured by pressure sensor 1. The static pressure of branch manifold 3 P3 was calculated from P1 and the data from differential pressure sensor 1. The static pressure of branch manifold 2 P2 was calculated from P3 and the data from differential pressure sensor 2. The density and speed measurement at each branch manifold were ρ1, ρ2, ρ3, V1, V2, and V3.The static pressure loss coefficient from branch manifold 1 to branch manifold 3L13 can be calculated with the following equation:
(1)L13=P1-P3P3.The total pressure loss coefficientK13 can be calculated with the following equation:
(2)K13=(P1+(1/2)ρ1V12)-(P3+(1/2)ρ3V32)(1/2)ρ3V32.The static pressure loss coefficient from branch manifold 2 to branch manifold 3L23 can be calculated with the following equation:
(3)L23=P2-P3P3.The total pressure loss coefficientK23 can be calculated with the following equation:
(4)K23=(P2+(1/2)ρ2V22)-(P3+(1/2)ρ3V32)(1/2)ρ3V32.


## 3.1. Test Procedure

In the test, in order to prevent a compressor from surging, the purge valve was only opened 30%. By using a step motor, the compressor worked at three speeds: 9000 r/min, 12000 r/min, and 15000 r/min.At each compressor speed, the flow control valve 1 was fully closed first, while flow control valve 2 was fully opened. Then, the flow control valve 1 was gradually opened, while flow control valve 2 was kept fully opened, Finally, while keeping flow control valve 1 fully opened, close flow control valve 2 gradually from fully opened to fully closed. The valve lift for each test was 5 mm when the flow control valves were either opened or closed. In each of the situations, output signals from the 10 sensors were collected after the data was stable.


## 3.2. Data Processing Method

Firstly, using the data from pressure sensor 2, temperature sensor 4, and differential pressure sensor 3, calculate the mass flow of the public manifold. Then, using the data from the mass flow sensor under the experimental condition of flow control valve 1 fully closed and flow control valve 2 fully opened, correct the calculated mass flow of the public manifold.The mass flow of branch manifold 3m3 was obtained from correcting the mass flow of the public manifold. The mass flow of branch manifold 2 m2 was obtained from the mass flow sensor. The mass flow of branch manifold 1 m1 was obtained from m3-m2. The static pressure of branch manifold 1 P1 was measured by pressure sensor 1. The static pressure of branch manifold 3 P3 was calculated from P1 and the data from differential pressure sensor 1. The static pressure of branch manifold 2 P2 was calculated from P3 and the data from differential pressure sensor 2. The density and speed measurement at each branch manifold were ρ1, ρ2, ρ3, V1, V2, and V3.The static pressure loss coefficient from branch manifold 1 to branch manifold 3L13 can be calculated with the following equation:
(1)L13=P1-P3P3.The total pressure loss coefficientK13 can be calculated with the following equation:
(2)K13=(P1+(1/2)ρ1V12)-(P3+(1/2)ρ3V32)(1/2)ρ3V32.The static pressure loss coefficient from branch manifold 2 to branch manifold 3L23 can be calculated with the following equation:
(3)L23=P2-P3P3.The total pressure loss coefficientK23 can be calculated with the following equation:
(4)K23=(P2+(1/2)ρ2V22)-(P3+(1/2)ρ3V32)(1/2)ρ3V32.


## 4. Experimental Results and Discussions

### 4.1. Flow Pattern from Branch Manifold 1 to Branch Manifold 3

Figures4 and 5 show the flow rates in branch manifold 1 and branch manifold 3, respectively, for each working condition of the compressor.Figure 4
Flow rates in branch manifold 1.Figure 5
Flow rates in branch manifold 3.In Figure4, for each working condition of the compressor, the mass flow in branch manifold 1 initially increased, and then tended to stabilize, with the increase of the flow control valve lift. The mass flow mainly increased in branch manifold 1 when the valve was lifted from 0 to 60 mm. When the valve lift was more than 60 mm, the mass flow m1 remained unchanged. The reason is that when the valve was initially lifted, the pressure difference between before and after was very big and the mass flow in branch manifold 1 increased as the valve was lifted. Then when the valve lift reached 60 mm, the flow area of the valve was similar to the area of branch manifold. After that, when the valve lift continued to open, the mass flow in the branch manifold 1 was no longer determined by the lift of valve 1, but it was mainly decided by its own area.In Figure5, for each working condition of the compressor, with the increase of the lift of flow control valve, the mass flow in branch manifold 3 was almost unchanged, owing to the flow resistance characteristics of the entire piping system. For the entire piping system, firstly, the flow resistance of branch manifold 1 connects in series with the flow resistance of the flow control valve. Then, they connect in parallel with the flow resistance of branch manifold 2. Finally, they connect in series with the flow resistance of branch manifold 3. When flow control valve 1 is gradually lifted, the flow resistance of the whole piping system decreases, which leads the operating point of compressor moving towards the flow increased. The bleed valve opening has remained at 30%, and the increase in mass flow was mainly dependent on the bleed valve flow and the mass flow in branch manifold 3 changing little. As the compressor speed increases, the mass flow in branch manifold 3 increases, too.Contrasting Figures4 and 5, when flow control valves 1 and 2 were both opened, the mass flow in branch manifold 1 was less than the mass flow in branch manifold 2. The reason is that the flow resistance of the piping system from the public manifold outlet to branch manifold 1 outlet is greater.When the compressor speed was constant and the mass flow in branch manifold 3 was small, the Mach number in branch manifold 3 changed little. The Mach number in branch manifold 3 was calculated and defined asM3. According to the pipe system configuration, the Mach number M3 was 0.25, 0.34, and 0.45 under compressor speeds of 9000 r/min, 12000 r/min and 15000 r/min. M3 can be used as a substitute for the compressor speed in the following research.


### 4.2. Experimental Pressure Loss from Branch Manifold 1 to Branch Manifold 3

For each working condition of the compressor, the comparison of the pressure difference from branch manifold 1 to branch manifold 3 is shown in Figure6. The comparison of the static pressure loss coefficient from branch manifold 1 to branch manifold 3, L13, is shown in Figure 7. The comparison of the total pressure loss coefficient from branch manifold 1 to branch manifold 3, K13, is shown in Figure 8.Figure 6
Pressure difference from branch manifold 1 to branch manifold 3.Figure 7
Static pressure loss coefficient from branch manifold 1 to branch manifold 3.Figure 8
Total pressure loss coefficient from branch manifold 1 to branch manifold 3.As can be seen from Figure6, the variation for the three pressure difference curves was consistent. When the Mach number M3 was a fixed value, the pressure difference between branch manifold 1 and branch manifold 3 first increased and then decreased with the increase of mass flow ratio of junctions 1 and 3. When the flow rate was constant, the pressure difference between branch manifold 1 and branch manifold 3 increased with the Mach number M3.As can be seen from Figure7, the variation of the three static pressure loss coefficients was the same as the variation for the pressure difference curves in Figure 6. When the Mach number M3 was a fixed value, the static pressure loss coefficient L13 first increased and then decreased with the increase of mass flow ratio of junctions 1 and 3. When the flow ratio was constant, the static pressure loss coefficient L13 increased along with an increasing Mach number M3.As can be seen from Figure8, the variation of the three total pressure loss coefficients was the same. The total pressure loss coefficient K13 always increased with the increase of the flow ratio between branch manifold 1 and branch manifold 3. When the flow ratio between branch manifold 1 and branch manifold 3 was equal to 0, the total pressure loss coefficient K13 was negative. The reason for this was that the mass flow of branch manifold 1 was equal to 0 and the air in branch manifold 2 had an extraction effect on the air in branch manifold 1, which leads the pressure in branch manifold 1 to decrease. When the flow ratio was equal to 0, the total pressure loss coefficient K13 increased alone with the decrease of the Mach number M3. This is because the flow rate in branch manifold 3 increased at the same time as the Mach number M3 and the increased flow rate in branch manifold 3 leads to a greater suction effect on the air in branch manifold 1. When the flow ratio between branch manifold 1 and branch manifold 3 was equal to 1, the higher the Mach number M3, the higher the total pressure loss coefficient K13. This was due to the greater flow ratio leading to a greater incidence loss, which was a part of the energy loss.


### 4.3. Experimental Pressure Loss from Branch Manifold 2 to Branch Manifold 3

For each working condition of the compressor, a comparison of the pressure difference from branch manifold 2 to branch manifold 3 is shown in Figure9. A comparison of the static pressure loss coefficient L23 is shown in Figure 10. A comparison of the total pressure loss coefficient K23 is shown in Figure 11.Figure 9
Pressure difference from branch manifold 2 to branch manifold 3.Figure 10
Static pressure loss coefficient from branch manifold 2 to branch manifold 3.Figure 11
Total pressure loss coefficient from branch manifold 2 to branch manifold 3.As can be seen from Figure9, the variation of the three pressure difference curves was consistent. When the Mach number M3 was a fixed value, the pressure difference between branch manifold 2 and branch manifold 3 first increased and then decreased as the flow ratio between branch manifold 2 and branch manifold 3 increased. When the flow ratio was constant, the pressure difference between branch manifold 2 and branch manifold 3 increased as did the Mach number M3.As can be seen from Figure10, the variation of the three static pressure loss coefficients was the same as the variation for the pressure difference curves in Figure 9. When the Mach number M3 was a fixed value, the static pressure loss coefficient L23 first increased and then decreased as the flow ratio between branch manifold 2 and branch manifold 3 increased. When the flow ratio was constant, the static pressure loss coefficient L23 increased with the Mach number M3.As can be seen from Figure11, the variation of the three total pressure loss coefficients was the same. When the Mach number M3 was a fixed value, the total pressure loss coefficient K23 increased along with the flow ratio between branch manifold 2 and branch manifold 3 increasing first and then decreased when the flow ratio reached 0.7. When the flow ratio between branch manifold 1 and branch manifold 3 was 0, the total pressure loss coefficient K23 increased with the Mach number M3. This was due to a greater incidence of loss between branch manifold 1 and branch manifold 3 when the Mach number M3 increased, which resulted in a decrease in the total pressure in branch manifold 3. When the flow ratio between branch manifold 2 and branch manifold 3 was equal to 1, the total pressure loss coefficient K23 increased with the Mach number M3. That was because there was no air flow in branch manifold 1, and the flow rate between branch manifold 2 and branch manifold 3 was the same. The total pressure loss coefficient K23 mainly depended on the local pressure loss in branch manifold 1 and its effect on branch manifold 2.Contrast Figure10 with Figure 11, and it can be determined that the maximum value of the static pressure loss coefficient L23 and the total pressure loss coefficient K23 are obtained at the same flow ratio 0.7. This was due to the impact loss of flow between branch manifold 1 and branch manifold 2 having the largest effect on the air’s energy loss in branch manifold 2 at that moment.Contrast Figure7 with Figure 10, and it can be determined that the maximum value of the static pressure loss coefficient L13 appeared when the flow ratio between branch manifold 1 and branch manifold 3 was equal to 0.3. In addition, the maximum value of the static pressure loss coefficient L23 appeared when the flow ratio between branch manifold 2 and branch manifold 3 was equal to 0.7. The maximum values of L13 and L23 as well as K23, the total pressure loss coefficient, all appeared at the same condition.Contrast Figure8 with Figure 11, and it can be determined that when the flow ratio was unchanged, the total pressure loss coefficient K23 was strongly influenced by the Mach number M3.


## 4.1. Flow Pattern from Branch Manifold 1 to Branch Manifold 3

Figures4 and 5 show the flow rates in branch manifold 1 and branch manifold 3, respectively, for each working condition of the compressor.Figure 4
Flow rates in branch manifold 1.Figure 5
Flow rates in branch manifold 3.In Figure4, for each working condition of the compressor, the mass flow in branch manifold 1 initially increased, and then tended to stabilize, with the increase of the flow control valve lift. The mass flow mainly increased in branch manifold 1 when the valve was lifted from 0 to 60 mm. When the valve lift was more than 60 mm, the mass flow m1 remained unchanged. The reason is that when the valve was initially lifted, the pressure difference between before and after was very big and the mass flow in branch manifold 1 increased as the valve was lifted. Then when the valve lift reached 60 mm, the flow area of the valve was similar to the area of branch manifold. After that, when the valve lift continued to open, the mass flow in the branch manifold 1 was no longer determined by the lift of valve 1, but it was mainly decided by its own area.In Figure5, for each working condition of the compressor, with the increase of the lift of flow control valve, the mass flow in branch manifold 3 was almost unchanged, owing to the flow resistance characteristics of the entire piping system. For the entire piping system, firstly, the flow resistance of branch manifold 1 connects in series with the flow resistance of the flow control valve. Then, they connect in parallel with the flow resistance of branch manifold 2. Finally, they connect in series with the flow resistance of branch manifold 3. When flow control valve 1 is gradually lifted, the flow resistance of the whole piping system decreases, which leads the operating point of compressor moving towards the flow increased. The bleed valve opening has remained at 30%, and the increase in mass flow was mainly dependent on the bleed valve flow and the mass flow in branch manifold 3 changing little. As the compressor speed increases, the mass flow in branch manifold 3 increases, too.Contrasting Figures4 and 5, when flow control valves 1 and 2 were both opened, the mass flow in branch manifold 1 was less than the mass flow in branch manifold 2. The reason is that the flow resistance of the piping system from the public manifold outlet to branch manifold 1 outlet is greater.When the compressor speed was constant and the mass flow in branch manifold 3 was small, the Mach number in branch manifold 3 changed little. The Mach number in branch manifold 3 was calculated and defined asM3. According to the pipe system configuration, the Mach number M3 was 0.25, 0.34, and 0.45 under compressor speeds of 9000 r/min, 12000 r/min and 15000 r/min. M3 can be used as a substitute for the compressor speed in the following research.


## 4.2. Experimental Pressure Loss from Branch Manifold 1 to Branch Manifold 3

For each working condition of the compressor, the comparison of the pressure difference from branch manifold 1 to branch manifold 3 is shown in Figure6. The comparison of the static pressure loss coefficient from branch manifold 1 to branch manifold 3, L13, is shown in Figure 7. The comparison of the total pressure loss coefficient from branch manifold 1 to branch manifold 3, K13, is shown in Figure 8.Figure 6
Pressure difference from branch manifold 1 to branch manifold 3.Figure 7
Static pressure loss coefficient from branch manifold 1 to branch manifold 3.Figure 8
Total pressure loss coefficient from branch manifold 1 to branch manifold 3.As can be seen from Figure6, the variation for the three pressure difference curves was consistent. When the Mach number M3 was a fixed value, the pressure difference between branch manifold 1 and branch manifold 3 first increased and then decreased with the increase of mass flow ratio of junctions 1 and 3. When the flow rate was constant, the pressure difference between branch manifold 1 and branch manifold 3 increased with the Mach number M3.As can be seen from Figure7, the variation of the three static pressure loss coefficients was the same as the variation for the pressure difference curves in Figure 6. When the Mach number M3 was a fixed value, the static pressure loss coefficient L13 first increased and then decreased with the increase of mass flow ratio of junctions 1 and 3. When the flow ratio was constant, the static pressure loss coefficient L13 increased along with an increasing Mach number M3.As can be seen from Figure8, the variation of the three total pressure loss coefficients was the same. The total pressure loss coefficient K13 always increased with the increase of the flow ratio between branch manifold 1 and branch manifold 3. When the flow ratio between branch manifold 1 and branch manifold 3 was equal to 0, the total pressure loss coefficient K13 was negative. The reason for this was that the mass flow of branch manifold 1 was equal to 0 and the air in branch manifold 2 had an extraction effect on the air in branch manifold 1, which leads the pressure in branch manifold 1 to decrease. When the flow ratio was equal to 0, the total pressure loss coefficient K13 increased alone with the decrease of the Mach number M3. This is because the flow rate in branch manifold 3 increased at the same time as the Mach number M3 and the increased flow rate in branch manifold 3 leads to a greater suction effect on the air in branch manifold 1. When the flow ratio between branch manifold 1 and branch manifold 3 was equal to 1, the higher the Mach number M3, the higher the total pressure loss coefficient K13. This was due to the greater flow ratio leading to a greater incidence loss, which was a part of the energy loss.


## 4.3. Experimental Pressure Loss from Branch Manifold 2 to Branch Manifold 3

For each working condition of the compressor, a comparison of the pressure difference from branch manifold 2 to branch manifold 3 is shown in Figure9. A comparison of the static pressure loss coefficient L23 is shown in Figure 10. A comparison of the total pressure loss coefficient K23 is shown in Figure 11.Figure 9
Pressure difference from branch manifold 2 to branch manifold 3.Figure 10
Static pressure loss coefficient from branch manifold 2 to branch manifold 3.Figure 11
Total pressure loss coefficient from branch manifold 2 to branch manifold 3.As can be seen from Figure9, the variation of the three pressure difference curves was consistent. When the Mach number M3 was a fixed value, the pressure difference between branch manifold 2 and branch manifold 3 first increased and then decreased as the flow ratio between branch manifold 2 and branch manifold 3 increased. When the flow ratio was constant, the pressure difference between branch manifold 2 and branch manifold 3 increased as did the Mach number M3.As can be seen from Figure10, the variation of the three static pressure loss coefficients was the same as the variation for the pressure difference curves in Figure 9. When the Mach number M3 was a fixed value, the static pressure loss coefficient L23 first increased and then decreased as the flow ratio between branch manifold 2 and branch manifold 3 increased. When the flow ratio was constant, the static pressure loss coefficient L23 increased with the Mach number M3.As can be seen from Figure11, the variation of the three total pressure loss coefficients was the same. When the Mach number M3 was a fixed value, the total pressure loss coefficient K23 increased along with the flow ratio between branch manifold 2 and branch manifold 3 increasing first and then decreased when the flow ratio reached 0.7. When the flow ratio between branch manifold 1 and branch manifold 3 was 0, the total pressure loss coefficient K23 increased with the Mach number M3. This was due to a greater incidence of loss between branch manifold 1 and branch manifold 3 when the Mach number M3 increased, which resulted in a decrease in the total pressure in branch manifold 3. When the flow ratio between branch manifold 2 and branch manifold 3 was equal to 1, the total pressure loss coefficient K23 increased with the Mach number M3. That was because there was no air flow in branch manifold 1, and the flow rate between branch manifold 2 and branch manifold 3 was the same. The total pressure loss coefficient K23 mainly depended on the local pressure loss in branch manifold 1 and its effect on branch manifold 2.Contrast Figure10 with Figure 11, and it can be determined that the maximum value of the static pressure loss coefficient L23 and the total pressure loss coefficient K23 are obtained at the same flow ratio 0.7. This was due to the impact loss of flow between branch manifold 1 and branch manifold 2 having the largest effect on the air’s energy loss in branch manifold 2 at that moment.Contrast Figure7 with Figure 10, and it can be determined that the maximum value of the static pressure loss coefficient L13 appeared when the flow ratio between branch manifold 1 and branch manifold 3 was equal to 0.3. In addition, the maximum value of the static pressure loss coefficient L23 appeared when the flow ratio between branch manifold 2 and branch manifold 3 was equal to 0.7. The maximum values of L13 and L23 as well as K23, the total pressure loss coefficient, all appeared at the same condition.Contrast Figure8 with Figure 11, and it can be determined that when the flow ratio was unchanged, the total pressure loss coefficient K23 was strongly influenced by the Mach number M3.


## 5. Junction Simulation and Discussions

### 5.1.  45° Junction Simulation

As the flow phenomena in the manifold could not be reflect by experiment, the flow field of junction was simulated by AVL-Fire. The size of simulation model was the same as the measured model which is showed in Figure12. The inlet boundary conditions of branch manifolds 1 and 2 were mass flow, and the outlet boundary condition of branch manifold 3 was atmospheric pressure. The Mach numbers in branch manifold 3 M3 were 0.25, 0.34, and 0.45. For each working condition, the flow ratio between branch manifold 1 and branch manifold 3 Q13 changed from 0 to 1.Figure 12
Simulation model of junction.The comparison of total pressure loss coefficient between calculated and measured values was showed in Figure13. The values calculated by CFD were in good agreement with experimental observations. When the flow ratio between branch manifold 1 and branch manifold 3 Q13 was equal to 0, the junction could be seen as straight pipe. Since the influence of branch manifold 1 can be ignored, the calculated values almost equal to measured values. With the increase of flow rate in branch manifold 1, simulation data were slightly less than the test data, but the change trend of the calculated values were the same as the measured values. Simulation results could reflect the change trend of total pressure loss coefficients K13 and K23. As can be seen from Figure 13, the calculated value of total pressure loss coefficient K13 always increased when the flow ratio between branch manifold 1 and branch manifold 3 increased, which is the same as the measured value. The calculated value of total pressure loss coefficient K23 first increased and then decreased when the flow ratio between branch manifold 2 and branch manifold 3 reached 0.7.Comparison of total pressure loss coefficient between calculated and measured values.
(a)
K
13
(b)
K
23By using CFD analysis software, the internal flow phenomenon of junction could be analyzed. Figure14 shows the velocity fields of junction flow with different mass flow ratio at M3=0.34. The mass flow ratio between branch manifold 1 and branch manifold 3 Q13 changed from 0 to 1 at the same time when the mass flow ratio between branch manifold 2 and branch manifold 3 Q23 changed from 1 to 0. The uniformity of flow at branch joint is increased with the increase of the flow in branch manifold 1. When the mass flow ratio Q13 reached 0.6, vortex appeared in the junction and becomes stronger with the increase of Q13. Meanwhile, as can be seen from velocity fields of the junction, the flow impact from branch manifold 1 to branch manifold 2 was enhanced with the increase of Q13. Because of the above reasons, the total pressure loss coefficient K13 always increased with the increase of Q13. When the mass flow ratio Q23 was equal to 1, the total pressure loss coefficient K23 mainly depended on the local pressure loss in branch manifold 1 and its effect on branch manifold 2. Since the total pressure value of branch manifold 2 decreased with the reduction of flow rate, the total pressure loss coefficient K23 decreased alone with the decrease of the flow ratio Q23.Velocity flow fields of junction with different ratio of flow rate atM3=0.34.
(a)
Q
13
=
0
(
Q
23
=
0
)
(b)
Q
13
=
0.3
(
Q
23
=
0.7
)
(c)
Q
13
=
0.5
(
Q
23
=
0.5
)
(d)
Q
13
=
0.7
(
Q
23
=
0.3
)
(e)
Q
13
=
0.9
(
Q
23
=
0.1
)
(f)
Q
13
=
1
(
Q
23
=
0
)The comparison of simulation and test results showed that the following.(1)
Simulation could reflect the change trend of total pressure loss coefficient, but it could not predict its value accurately.(2)
It is necessary to carry out the experimental study to obtain the accurate value of the total pressure loss coefficient.


### 5.2.  30° and 60° Junction Simulation

As 45° junction is a common type in the exhaust system, the test was based on this type of manifold. But the angle between the branch manifold 1 and the branch manifold 2 may affects the flow condition in the manifold, and other structures also should be studied. As simulation results could reflect the change trend of total pressure loss coefficient, CFD analysis software was used to analyze the effect of branch angle on total pressure loss coefficient. Based on the previous studies, simulation models of 30° and 60° junction were set up. The boundary conditions of the models were the same as 45° junction, and the Mach number in branch manifold 3M3 was 0.34. Figure 15 shows the comparison of calculated total pressure loss coefficient with various lateral branch angles. As can be seen from the figures, when the branch manifold 1 was at low mass flow rate (the branch manifold 1 has less effect on branch manifolds 2 and 3), total pressure loss coefficients of different angles were almost the same. With the increase of mass flow rate of branch manifold 1 and the reduction of mass flow rate of branch manifold 2, the differences between different structures of the manifold are obvious. When the branch manifold 1 was at high mass flow rate, the greater the lateral branch angle, the greater the total pressure loss coefficients K13 and K23.Comparison of calculated total pressure loss coefficient with various lateral branch angles.
(a)
K
13
(b)
K
23Velocity fields of junction flow with different lateral branch angles atQ13=0.9 and M3=0.34 are shown in Figure 16. The uniformity of flow at branch joint is increased with the increase of lateral branch angle, and the flow impact between branch manifolds 1 and 2 increased significantly. Meanwhile, vortex appeared in the junction, and it becomes stronger with the increase of the lateral branch angle. For the above reasons, the total pressure loss coefficient K13 increased alone with the increase of lateral branch angle.Velocity flow fields of junction with different lateral branch angles atQ13=0.9, and M3=0.34.
(a)
30° junction
(b)
45° junction
(c)
60° junction


## 5.1.  45° Junction Simulation

As the flow phenomena in the manifold could not be reflect by experiment, the flow field of junction was simulated by AVL-Fire. The size of simulation model was the same as the measured model which is showed in Figure12. The inlet boundary conditions of branch manifolds 1 and 2 were mass flow, and the outlet boundary condition of branch manifold 3 was atmospheric pressure. The Mach numbers in branch manifold 3 M3 were 0.25, 0.34, and 0.45. For each working condition, the flow ratio between branch manifold 1 and branch manifold 3 Q13 changed from 0 to 1.Figure 12
Simulation model of junction.The comparison of total pressure loss coefficient between calculated and measured values was showed in Figure13. The values calculated by CFD were in good agreement with experimental observations. When the flow ratio between branch manifold 1 and branch manifold 3 Q13 was equal to 0, the junction could be seen as straight pipe. Since the influence of branch manifold 1 can be ignored, the calculated values almost equal to measured values. With the increase of flow rate in branch manifold 1, simulation data were slightly less than the test data, but the change trend of the calculated values were the same as the measured values. Simulation results could reflect the change trend of total pressure loss coefficients K13 and K23. As can be seen from Figure 13, the calculated value of total pressure loss coefficient K13 always increased when the flow ratio between branch manifold 1 and branch manifold 3 increased, which is the same as the measured value. The calculated value of total pressure loss coefficient K23 first increased and then decreased when the flow ratio between branch manifold 2 and branch manifold 3 reached 0.7.Comparison of total pressure loss coefficient between calculated and measured values.
(a)
K
13
(b)
K
23By using CFD analysis software, the internal flow phenomenon of junction could be analyzed. Figure14 shows the velocity fields of junction flow with different mass flow ratio at M3=0.34. The mass flow ratio between branch manifold 1 and branch manifold 3 Q13 changed from 0 to 1 at the same time when the mass flow ratio between branch manifold 2 and branch manifold 3 Q23 changed from 1 to 0. The uniformity of flow at branch joint is increased with the increase of the flow in branch manifold 1. When the mass flow ratio Q13 reached 0.6, vortex appeared in the junction and becomes stronger with the increase of Q13. Meanwhile, as can be seen from velocity fields of the junction, the flow impact from branch manifold 1 to branch manifold 2 was enhanced with the increase of Q13. Because of the above reasons, the total pressure loss coefficient K13 always increased with the increase of Q13. When the mass flow ratio Q23 was equal to 1, the total pressure loss coefficient K23 mainly depended on the local pressure loss in branch manifold 1 and its effect on branch manifold 2. Since the total pressure value of branch manifold 2 decreased with the reduction of flow rate, the total pressure loss coefficient K23 decreased alone with the decrease of the flow ratio Q23.Velocity flow fields of junction with different ratio of flow rate atM3=0.34.
(a)
Q
13
=
0
(
Q
23
=
0
)
(b)
Q
13
=
0.3
(
Q
23
=
0.7
)
(c)
Q
13
=
0.5
(
Q
23
=
0.5
)
(d)
Q
13
=
0.7
(
Q
23
=
0.3
)
(e)
Q
13
=
0.9
(
Q
23
=
0.1
)
(f)
Q
13
=
1
(
Q
23
=
0
)The comparison of simulation and test results showed that the following.(1)
Simulation could reflect the change trend of total pressure loss coefficient, but it could not predict its value accurately.(2)
It is necessary to carry out the experimental study to obtain the accurate value of the total pressure loss coefficient.


## 5.2.  30° and 60° Junction Simulation

As 45° junction is a common type in the exhaust system, the test was based on this type of manifold. But the angle between the branch manifold 1 and the branch manifold 2 may affects the flow condition in the manifold, and other structures also should be studied. As simulation results could reflect the change trend of total pressure loss coefficient, CFD analysis software was used to analyze the effect of branch angle on total pressure loss coefficient. Based on the previous studies, simulation models of 30° and 60° junction were set up. The boundary conditions of the models were the same as 45° junction, and the Mach number in branch manifold 3M3 was 0.34. Figure 15 shows the comparison of calculated total pressure loss coefficient with various lateral branch angles. As can be seen from the figures, when the branch manifold 1 was at low mass flow rate (the branch manifold 1 has less effect on branch manifolds 2 and 3), total pressure loss coefficients of different angles were almost the same. With the increase of mass flow rate of branch manifold 1 and the reduction of mass flow rate of branch manifold 2, the differences between different structures of the manifold are obvious. When the branch manifold 1 was at high mass flow rate, the greater the lateral branch angle, the greater the total pressure loss coefficients K13 and K23.Comparison of calculated total pressure loss coefficient with various lateral branch angles.
(a)
K
13
(b)
K
23Velocity fields of junction flow with different lateral branch angles atQ13=0.9 and M3=0.34 are shown in Figure 16. The uniformity of flow at branch joint is increased with the increase of lateral branch angle, and the flow impact between branch manifolds 1 and 2 increased significantly. Meanwhile, vortex appeared in the junction, and it becomes stronger with the increase of the lateral branch angle. For the above reasons, the total pressure loss coefficient K13 increased alone with the increase of lateral branch angle.Velocity flow fields of junction with different lateral branch angles atQ13=0.9, and M3=0.34.
(a)
30° junction
(b)
45° junction
(c)
60° junction


## 6. Conclusions

The high speed flow in a diesel exhaust manifold 45° junction was tested, and three junctions with different lateral branch angles were simulated by CFD analysis software. The steady experimental and simulated results indicated that the following.(1)
The static pressure loss coefficientL13 first increased and then decreased along with the flow ratio between branch manifold 1 and branch manifold 3 increasing; the variation law of the static pressure loss coefficient L23 was similar to L13.(2)
The total pressure loss coefficientK13 always increased with the increase of the flow ratio between branch manifold 1 and branch manifold 3; the total pressure loss coefficient K23 first increased and then decreased with the increase of the flow ratio between branch manifold 2 and branch manifold 3.(3)
The maximum values for the static pressure loss coefficientL13, the static pressure loss coefficient L23, and the total pressure loss coefficient K13 appeared at exactly the same condition.(4)
When the flow ratio was unchanged, the total pressure loss coefficientK23 was strongly influenced by the Mach number M3.(5)
Simulation results predicted the change trend of total pressure loss coefficient, but they could not predict their value accurately. It is necessary to carry out the experimental study to obtain the accurate value of the total pressure loss coefficient.(6)
When the branch manifold 1 was at low mass flow rate, total pressure loss coefficients of different branch angles were almost the same. At high mass flow rate, the total pressure loss coefficients increased alone with the increase of lateral branch angle.



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*Source: 316498-2014-03-13.xml*