# SIDLAB References 3

Flow and Pressure Drop Calculation Using Two-Ports

Elnady, T., Elsaadany, S., and Åbom, M., “Flow and Pressure Drop Calculation Using Two-Ports,” J. Vib. Acoust. 133(4):8, 2011, doi:10.1115/1.4003593.

### Abstract

Exhaust systems should be carefully designed for different applications. The main objective of an exhaust system is to reduce the engine noise. Maximum noise reduction is usually desired to the limit of a certain backpressure, which is set by the engine manufacturer in order not to deteriorate the engine efficiency. Therefore, a parallel calculation of the flow and pressure drop must be performed. The amount of flow flowing through each element will also affect its acoustic properties. Usually, acoustic and flow calculations are done separately on two different software. This paper describes a new technique that enables both calculations to be done using the same input data on the same platform. Acoustic calculations are usually performed in the frequency domain in the plane wave region using the two-port theory and then the acoustic pressure in the system is solved for using well-known algorithms to handle arbitrary connected two-ports. The stagnation pressure and volume flow can also be calculated using the same algorithm by deriving a flow two-port for each element using the stagnation pressure and the volume flow velocity as the state variables. The proposed theory is first discussed listing the flow matrices for common elements in exhaust elements, and then different systems are analyzed and compared with the measurements.

### Application

In order to accurately simulate the sound propagation inside complex duct networks in the presence of flow, it is important to know the flow distribution inside different parts of the network. It is well known that air flow inside a duct has a large effect on the acoustic properties of different network elements. For example, when flow is introduced through a muffler, its transmission properties are affected in three different ways. The first is through the convective effects, which affect the propagation inside straight duct sections. The second is the introduction of extra losses at area expansions and contractions. The third and most important effect of flow is introduced by the change of the perforate impedance. The flow can be either grazing to the perforate, through the perforate, or both.In the automotive industry, acoustic and flow calculations are done concurrently using a 1D time domain based engine cycle simulation tool such as GT POWER, WAVE, and AVL BOOST. This is not sufficient to properly design the exhaust system in the frequency domain; in particular, the handling of elements where dissipative effects are important, e.g., catalytic converters can be done more accurately in frequency domain codes. Also, acoustic optimization requiring iterative solutions of a large number of system modifications can be done much more effectively using linear frequency domain methods. Therefore, for the past decade, GT POWER, WAVE, and AVL BOOST have added frequency domain two-port models to their platforms, which is exactly the same technique used by this paper. As demonstrated here, it is possible to incorporate flow calculations in the two-port models, thereby making the frequency domain approach as complete as the time domain approach.

### Experimental Validation

The two-port technique above was implemented for several cases and compared with measurements. Three of these cases are shown below.

#### Through Muffler

This is a simple through flow muffler, as indicated in Fig. 1. The equivalent SIDLAB network is shown in Fig. 2. The perforated pipe is 1.4 mm thickness, has 4 mm hole diameter, and 12% porosity. The pressure-flow curve for this muffler is shown in Fig. 3.

Figure 1 Case 1: Schematic diagram of the through flow muffler

Figure 2 Case 1: SIDLAB network of the through flow muffler

Figure 3 Case 1: Pressure-flow curve of the through flow muffler

### Plug-Flow Mufflers

This muffler consists of two plugflow mufflers connected in series, as shown in Fig. 4. The equivalent SIDLAB network is shown in Fig. 5. The perforated pipe has a thickness of 1.2 mm and a hole diameter of 4 mm. Two cases with two perforation ratios are used: 7% and 28%. Figures 6 and 7 show the results for these cases compared with the measurements.

Figure 4 Case 2: Schematic diagram of the plug-flow muffler

Figure 5 Case 2: SIDLAB network of the plug-flow muffler

Figure 6 Case 2: Pressure-flow curve of the plug-flow muffler porosity of 7%

Figure 7 Case 2: Pressure-flow curve of the plug-flow muffler porosity of 28%

After Treatment Device.An after treatment device _ATD_ is used to reduce harmful emissions of diesel engines. The ATD characteristics must ensure a good compromise among high filtration efficiency, low-pressure drop, and good penetration/ dispersion of the soot particles inside the trap matrix. The ATD unit presented here is a real unit for a passenger car that uses a diesel engine. The ATD contains both catalytic converter and a diesel particulate filter. The layout of the ATD is shown in Fig. 8. The SIDLAB network is shown in Fig. 9. The pressure-flow curve for this device is shown in Fig. 10. The catalytic converter has a length of 0.08 m, diameter of 0.15 m, 400 cells/ in2, and wall thickness of 0.45 m. The diesel particulate filter has a length of 0.25 m, diameter of 0.15 m, 200 cells/ in2, and wall thickness of 0.355. The walls are assumed to have a ceramic permeability of 2.5×10−13 m2, and the soot is assumed to have a permeability of 1.5×10−14 m2. The properties of the rest of the elements are listed in Table 1.

Figure 8 Case 3: Schematic diagram of the after-treatment device

Figure 9 Case 3: SIDLAB network of the after-treatment device

Figure 10 Case 3: Pressure-flow curve of the after-treatment device