### Abstract

An integral method is presented for determining effects of buoyancy due to heat release on the properties of reacting jets and plumes. This method avoids the Morton entrainment hypothesis entirely, and thus removes the ad hoc 'entrainment modelling' required in most other integral approaches. We develop the integral equation for the local centreline velocity u_{c}(x), which allows modelling in terms of the local flow width δ(x). In both the momentum-dominated jet limit and buoyancy-dominated plume limit, dimensional arguments show δ(x) ∼ x, and experimental data show the proportionality factor c_{δ} to remain constant between these limits. The entrainment modelling required in traditional integral methods is thus replaced by the observed constant c_{δ} value in the present method. In non-reacting buoyant jets, this new integral approach provides an exact solution for u_{c}(x) that shows excellent agreement with experimental data, and gives simple expressions for the virtual origins of jets, plumes and buoyant jets. In the exothermically reacting case, the constant c_{δ} value gives an expression for the buoyancy flux (x) that allows the integral equation for u_{c}(x) to be solved for arbitrary exit conditions. The resulting u_{c}(x) determines the local mass, momentum and buoyancy fluxes throughout the flow, as well as the centreline mixture fraction ζ_{c}(x) and thus the flame length L. The latter provides the proper parameters Ω and Λ that determine buoyancy effects on the flame, and provides power-law scalings in the momentum-dominated and buoyancy-dominated limits. Comparisons with buoyant flame data show excellent agreement over a wide range of conditions.

Original language | English (US) |
---|---|

Pages (from-to) | 221-255 |

Number of pages | 35 |

Journal | Journal of Fluid Mechanics |

Volume | 575 |

DOIs | |

State | Published - Mar 25 2007 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

### Cite this

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**Effects of heat release on turbulent shear flows. Part 3. Buoyancy effects due to heat release in jets and plumes.** / Diez Garias, Francisco; Dahm, Werner J.A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Effects of heat release on turbulent shear flows. Part 3. Buoyancy effects due to heat release in jets and plumes

AU - Diez Garias, Francisco

AU - Dahm, Werner J.A.

PY - 2007/3/25

Y1 - 2007/3/25

N2 - An integral method is presented for determining effects of buoyancy due to heat release on the properties of reacting jets and plumes. This method avoids the Morton entrainment hypothesis entirely, and thus removes the ad hoc 'entrainment modelling' required in most other integral approaches. We develop the integral equation for the local centreline velocity uc(x), which allows modelling in terms of the local flow width δ(x). In both the momentum-dominated jet limit and buoyancy-dominated plume limit, dimensional arguments show δ(x) ∼ x, and experimental data show the proportionality factor cδ to remain constant between these limits. The entrainment modelling required in traditional integral methods is thus replaced by the observed constant cδ value in the present method. In non-reacting buoyant jets, this new integral approach provides an exact solution for uc(x) that shows excellent agreement with experimental data, and gives simple expressions for the virtual origins of jets, plumes and buoyant jets. In the exothermically reacting case, the constant cδ value gives an expression for the buoyancy flux (x) that allows the integral equation for uc(x) to be solved for arbitrary exit conditions. The resulting uc(x) determines the local mass, momentum and buoyancy fluxes throughout the flow, as well as the centreline mixture fraction ζc(x) and thus the flame length L. The latter provides the proper parameters Ω and Λ that determine buoyancy effects on the flame, and provides power-law scalings in the momentum-dominated and buoyancy-dominated limits. Comparisons with buoyant flame data show excellent agreement over a wide range of conditions.

AB - An integral method is presented for determining effects of buoyancy due to heat release on the properties of reacting jets and plumes. This method avoids the Morton entrainment hypothesis entirely, and thus removes the ad hoc 'entrainment modelling' required in most other integral approaches. We develop the integral equation for the local centreline velocity uc(x), which allows modelling in terms of the local flow width δ(x). In both the momentum-dominated jet limit and buoyancy-dominated plume limit, dimensional arguments show δ(x) ∼ x, and experimental data show the proportionality factor cδ to remain constant between these limits. The entrainment modelling required in traditional integral methods is thus replaced by the observed constant cδ value in the present method. In non-reacting buoyant jets, this new integral approach provides an exact solution for uc(x) that shows excellent agreement with experimental data, and gives simple expressions for the virtual origins of jets, plumes and buoyant jets. In the exothermically reacting case, the constant cδ value gives an expression for the buoyancy flux (x) that allows the integral equation for uc(x) to be solved for arbitrary exit conditions. The resulting uc(x) determines the local mass, momentum and buoyancy fluxes throughout the flow, as well as the centreline mixture fraction ζc(x) and thus the flame length L. The latter provides the proper parameters Ω and Λ that determine buoyancy effects on the flame, and provides power-law scalings in the momentum-dominated and buoyancy-dominated limits. Comparisons with buoyant flame data show excellent agreement over a wide range of conditions.

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U2 - 10.1017/S0022112006004277

DO - 10.1017/S0022112006004277

M3 - Article

VL - 575

SP - 221

EP - 255

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -