# Numerical Analysis of Engine Exhaust Flow Parameters for Resolving Pre-Turbine Pulsating Flow Enthalpy and Exergy

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Literature Review

#### 1.2. Objectives of the Present Work

- Enthalpy and exergy transport by the ICE exhaust pulsation were computed and compared in both specific and mass flow rate based forms.
- The analytical solutions of enthalpy and exergy sensitivities to flow parameters were derived and further analyzed in the context of engine exhaust conditions.
- Based on the results of local sensitivity analysis, the requirements of accurate and fast measurements (or estimation) for capturing the energy carried by exhaust pulses are discussed herein.
- The Sobol indices in global sensitivity analysis quantify the significance of flow parameters for evaluating flow enthalpy and exergy. Moreover, the interaction effects among flow parameters were also identified.

#### 1.3. Document Organization

## 2. Methodology

#### 2.1. Flow Enthalpy and Exergy

#### 2.2. Sensitivity Analyses

## 3. Engine Specifications and Numerical Simulation

## 4. Results and Discussion

#### 4.1. Enthalpy and Exergy Pulsations

#### 4.2. Cycle-Averaged Enthalpy and Exergy

#### 4.3. Effect of Exhaust Gas Composition

#### 4.4. Analytical Solutions for the Sensitivity to Flow Parameters

#### 4.5. Local Sensitivity

#### 4.6. Global Sensitivity

## 5. Conclusions

- Based on the exhaust flow conditions at different locations, it was found that the degrees of specific enthalpy and exergy fluctuation decreased from the exhaust valve to the turbine inlet. This can be explained by the reduced fluctuation of the respective flow parameters across the different locations due to expansion and pulse interaction effects. Moreover, the waveforms of flow enthalpy and exergy rates are determined by the instantaneous mass flow rate.
- For evaluating the cycle-averaged flow enthalpy and exergy using mean values of the flow parameters (representative of “slow measurements”), the need for high resolution flow parameters was indicated for accurate computations of the cycle-averaged enthalpy and exergy rates irrespective of the physical location and with greater error reduction potential towards stronger pulsating flow (from turbine inlet towards the exhaust valve). However, the errors in specific enthalpy and exergy computation appear to have less significance for high resolution flow parameters, especially in the turbine inlet conditions of the analyzed cases.
- The variations in exhaust gas composition had negligible impacts on the flow enthalpy and exergy quantification.
- The analytical solution revealed that flow temperature fluctuations are the most significant for computing specific enthalpy and exergy. However, pressure and velocity fluctuations are the primary factors for assessing the total enthalpy and exergy rates.
- For specific flow enthalpy and exergy, the effect of flow pressure mainly occurred at the low-p area of the pulse, whereas the influence of flow velocity was concentrated on the high-u region. As previously mentioned, temperature’s sensitivity was observable through the entirety of the exhaust pulse. Unlike the specific flow enthalpy and exergy, for the enthalpy and exergy rates, the deviations caused by the sweep of 5% flow parameter were minor, and the observed sensitivity mainly appeared at the peaks of exhaust pulses where the flow parameters were also at their peak values.
- As a representation of the responses of “slow” flow measurements, the cycle-averaged flow parameters were used in the local SA to illustrate the deviations of pulse shapes in terms of the flow enthalpy and exergy. A comparison of cycle-resolved and cycle-averaged flow parameters showed that high resolution temperature and velocity are required to accurately capture the specific enthalpy and exergy. However, when evaluating the total enthalpy and exergy rates, a high resolution of velocity is the most important, especially at locations before the exhaust manifold, and high resolution of the pressure pulse becomes necessary at the turbine inlet.
- Sobol indices in the global SA show that temperature contributed at least 88% sensitivity to specific enthalpy and 66.9% to specific exergy. Moreover, the specific exergy sensitivity to flow velocity was relatively larger than that of the the specific enthalpy. On the other hand, for enthalpy and exergy rates, the sensitivity of flow velocity was most significant for most cases. In addition, at the turbine inlet, the significance of pressure increased to 62% for enthalpy rate and 70% for exergy rate.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclatures

Abbreviations | |

ICE | Internal combustion engine |

nIMEP | Net indicated mean effective pressure |

BMEP | Brake mean effective pressure |

CA | Crank angle |

IVO | Intake valve opening |

IVC | Intake valve closing |

EVO | Exhaust valve opening |

EVC | Exhaust valve closing |

BBDC | Before bottom dead centre |

ATDC | After top dead centre |

SA | Sensitivity analysis |

MAPE | Maximum absolute percentage error |

Notations | |

H | Enthalpy rate [kW] |

E | Exergy rate [kW] |

h | Specific stagnation enthalpy [kJ/kg] |

e | Specific exergy [kJ/kg] |

s | Specific entropy [$\phantom{\rule{0.166667em}{0ex}}\mathrm{J}/(\mathrm{kg}\xb7\mathrm{K})$] |

$\dot{m}$ | Mass flow rate [kg/s] |

p | Static pressure [bar abs.] |

T | Static temperature [K] |

u | Flow velocity [m/s] |

${c}_{p}$ | Specific heat capacity [$\phantom{\rule{0.166667em}{0ex}}\mathrm{J}/(\mathrm{kg}\xb7\mathrm{K})$] |

${R}_{g}$ | Specific gas constant of gaseous mixture [$\phantom{\rule{0.166667em}{0ex}}\mathrm{J}/(\mathrm{kg}\xb7\mathrm{K})$] |

$\rho $ | Flow density [$\phantom{\rule{0.166667em}{0ex}}\mathrm{kg}/{\mathrm{m}}^{3}$] |

$\gamma $ | Heat capacity ratio [-] |

${a}_{i}$ | Coefficients of NASA polynomial |

M | Mach number [-] |

$\theta $ | Crank angle [${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$] |

$\tilde{H}$ | Mass flux based enthalpy rate [$\phantom{\rule{0.166667em}{0ex}}\mathrm{kW}/{\mathrm{m}}^{2}$] |

$\tilde{E}$ | Mass flux based exergy rate [$\phantom{\rule{0.166667em}{0ex}}\mathrm{kW}/{\mathrm{m}}^{2}$] |

A | Effective cross-sectional flow area [$\phantom{\rule{0.166667em}{0ex}}{\mathrm{mm}}^{2}$] |

$\varphi $ | Fuel–air equivalence ratio [-] |

${p}_{0}$ | Ambient pressure [bar abs.] |

${T}_{0}$ | Ambient temperature [K] |

$S{I}_{i}$ | Sobol main effect index for the ith component [%] |

$S{I}_{i}^{T}$ | Sobol total effect index for ith component [%] |

$\mathrm{V}(\xb7)$ | Variance of a variable |

$\mathrm{E}(\phantom{\rule{0.166667em}{0ex}}\xb7|x\phantom{\rule{0.166667em}{0ex}})$ | Conditional expected value with a given x |

$x,y$ | Input and output variables for sensitivity analysis |

## Appendix A. Exhaust Flow Parameters at Three Measurement Locations

## Appendix B. Derivation of Analytical Solutions

**Table A1.**Fuel–air equivalence ratio $\varphi $, mass-basis gas constant ${R}_{g}$ and specific heat capacity coefficients ${a}_{i}$ for exhaust gases at test points (a) and (b). The unit of ${R}_{g}$ and ${c}_{p}$ is: [J · kg${}^{-1}$· K${}^{-1}$].

$\mathit{\varphi}$ | ${\mathit{R}}_{\mathit{g}}$ | ${\mathit{a}}_{1}$ | ${\mathit{a}}_{2}\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{3}$ | ${\mathit{a}}_{3}\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{6}$ | ${\mathit{a}}_{4}\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{9}$ | ${\mathit{a}}_{5}\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{12}$ | |
---|---|---|---|---|---|---|---|

(a) | 0.532 | 289.191 | 3.511 | 0.065 | 0.968 | −0.132 | −0.191 |

(b) | 0.581 | 289.280 | 3.505 | 0.142 | 0.858 | −0.504 | −0.214 |

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**Figure 1.**An illustration of three locations (marked as red circles) for obtaining the exhaust pulsation in simulations. The blue squares denote the measuring points of exhaust flow in engine experiments.

**Figure 2.**Calibration of engine performance and exhaust conditions at engine operating points: (a) 1300 rpm/17.8 nIMEP; (b) 900 rpm/11.5 nIMEP. The dots denote the cycle-averaged values of engine parameters over one cycle from engine tests and numerical simulations.

**Figure 3.**A comparison of crank-angle-resolved exhaust static pressure between fast measurements from engine tests and numerical simulations at engine operating points: (a) 1300 rpm/17.8 nIMEP; (b) 900 rpm/11.5 nIMEP.

**Figure 4.**The effective area and valve lift of exhaust valve with the flow Mach number under two operating conditions: (a) 1300 rpm/17.8 nIMEP; (b) 900 rpm/11.5 nIMEP.

**Figure 5.**Specific enthalpy and exergy in exhaust pulsations at measurement positions operating at test points: (a) 1300 rpm/17.8 nIMEP; (b) 900 rpm/11.5 nIMEP.

**Figure 6.**Flow enthalpy and exergy of exhaust pulsations at three measurement positions operating at test points: (a) 1300 rpm/17.8 nIMEP; (b) 900 rpm/11.5 nIMEP.

**Figure 7.**The effect of fuel–air equivalent ratio ${\varphi}_{a}$ on the specific exergy at port outlet. Test point (a) 1300 rpm/17.8 nIMEP.

**Figure 8.**Gradient-based sensitivity of specific enthalpy and exergy (kJ/kg) with respect to flow parameters.

**Figure 9.**Gradient-based sensitivity of enthalpy and exergy flux (kW/m${}^{2}$) with respect to flow parameters. The normalization of flow parameters was performed by taking the mean values as: $\overline{T}=790$ K, $\overline{p}=2.5$ bar (abs.), and $\overline{u}=310$ m/s.

**Figure 10.**Local sensitivity analysis on the specific enthalpy and exergy pulsations (y-axis unit: kJ/kg) at the exhaust valve and operating at test point (a) 1300 rpm/17.8 nIMEP. From top to bottom, the shaded area in each subplot shows the deviations of enthalpy and exergy pulses caused by the variations in T, p, and u. The black curve represents the “true” enthalpy and exergy as a reference, while the dashed curves result from using the cycle-averaged value of each corresponding flow parameter.

**Figure 11.**MAPE for the specific enthalpy and exergy at test points (a) and (b). The solid markers represent enthalpy, and the hollow markers represent exergy.

**Figure 12.**Exergy rates (unit: kW) at the turbine inlet and operating at test point (b) 900 rpm/11.5 nIMEP. From top to bottom, the shaded area in each subplot shows the deviations in enthalpy and exergy pulses caused by the variations in T, p, and u. The black curve represents the “true” exergy rates of the exergy pulsation as a reference, and the dashed curves are results of using the cycle-averaged values of each corresponding flow parameter.

**Figure 13.**MAPE for enthalpy and exergy rates at test points. The solid markers represent enthalpy, and the hollow markers denote exergy.

**Figure 14.**The significance of flow parameters for specific enthalpy and exergy at the tested operating points. The solid bars represent enthalpy, and the hollow bars are for exergy.

**Figure 15.**The significance of flow parameters on enthalpy and exergy rates at the tested operating points. The solid bars represent enthalpy, and the hollow bars are for exergy.

Engine type | Scania D13 |

Cylinder layout | 6 inline |

Bore × Stroke | 130 mm × 160 mm |

Compression ratio | 18:1 |

Displacement | 12.7 L |

IVO/IVC | 18 ${}^{\circ}$CA BTDC/45 ${}^{\circ}$CA ABDC |

EVO/EVC | 55 ${}^{\circ}$CA BBDC/13 ${}^{\circ}$CA ATDC |

Fuel system | Common rail |

Turbocharger | Honeywell GT-4594 |

Emission standard | Euro VI |

Test Point (a) | Test Point (b) | |
---|---|---|

Speed [rpm] | 1300 | 900 |

nIMEP [bar] | 17.8 | 11.5 |

Load [kW] | 245 | 110 |

Fuel mass injected [mg/cylinder] | 202 | 136 |

Intake air flow [kg/s] | 0.22 | 0.10 |

Exhaust Valve | Port Outlet | Turbine Inlet | |
---|---|---|---|

Effective area A [mm${}^{2}$] | [0, 566.8] | 692.7 | 1612.1 |

(a) | Specific Enthalpy [kJ/kg] | Enthalpy Rate [kW] | Specific Exergy [kJ/kg] | Exergy Rate [kW] | ||||
---|---|---|---|---|---|---|---|---|

$\overline{\mathit{h}(\mathit{T},\mathit{p},\mathit{u})}$ | Error | $\overline{\mathit{H}(\mathit{T},\mathit{p},\mathit{u})}$ | Error | $\overline{\mathit{e}(\mathit{T},\mathit{p},\mathit{u})}$ | Error | $\overline{\mathit{E}(\mathit{T},\mathit{p},\mathit{u})}$ | Error | |

Exhaust valve | 585.9 | −2.4% | 18.8 | −62.4% | 334.4 | −4.2% | 11.2 | −65.8% |

Port outlet | 561.0 | −0.4% | 36.1 | −7.4% | 308.1 | −0.7% | 20.2 | −11.1% |

Turbine inlet | 544.2 | −0.1% | 103.7 | −1.9% | 291.5 | 0.1% | 56.9 | −2.7% |

(b) | Specific Enthalpy [kJ/kg] | Enthalpy Rate [kW] | Specific Exergy [kJ/kg] | Exergy Rate [kW] | ||||

$\overline{\mathit{h}(\mathit{T},\mathit{p},\mathit{u})}$ | Error | $\overline{\mathit{H}(\mathit{T},\mathit{p},\mathit{u})}$ | Error | $\overline{\mathit{e}(\mathit{T},\mathit{p},\mathit{u})}$ | Error | $\overline{\mathit{E}(\mathit{T},\mathit{p},\mathit{u})}$ | Error | |

Exhaust valve | 584.3 | −2.7% | 8.4 | −60.3% | 267.5 | −5.8% | 4.5 | −67.3% |

Port outlet | 536.0 | −0.5% | 16.9 | −13.6% | 245.9 | −0.6% | 8.3 | −22.2% |

Turbine inlet | 529.0 | −0.2% | 46.8 | −5.6% | 234.5 | 0.0% | 22.1 | −8.4 % |

O_{2} | N_{2} | CO_{2} | H_{2}O | ||

Test point (a) | ${\varphi}_{a}$ = 0.532 | 0.0946 | 0.7601 | 0.0697 | 0.0758 |

Test point (b) | ${\varphi}_{b}$ = 0.581 | 0.0843 | 0.7574 | 0.0760 | 0.0829 |

Stoichiometry | $\varphi $ = 1 | 0 | 0.7361 | 0.1269 | 0.1375 |

Air | $\varphi $ = 0 | 0.2101 | 0.7899 | 0 | 0 |

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**MDPI and ACS Style**

Hong, B.; Venkataraman, V.; Cronhjort, A. Numerical Analysis of Engine Exhaust Flow Parameters for Resolving Pre-Turbine Pulsating Flow Enthalpy and Exergy. *Energies* **2021**, *14*, 6183.
https://doi.org/10.3390/en14196183

**AMA Style**

Hong B, Venkataraman V, Cronhjort A. Numerical Analysis of Engine Exhaust Flow Parameters for Resolving Pre-Turbine Pulsating Flow Enthalpy and Exergy. *Energies*. 2021; 14(19):6183.
https://doi.org/10.3390/en14196183

**Chicago/Turabian Style**

Hong, Beichuan, Varun Venkataraman, and Andreas Cronhjort. 2021. "Numerical Analysis of Engine Exhaust Flow Parameters for Resolving Pre-Turbine Pulsating Flow Enthalpy and Exergy" *Energies* 14, no. 19: 6183.
https://doi.org/10.3390/en14196183