I Foundations基礎→
II Reacting Flows反應流→
III Premixed預混→
IV Non-Premixed非預混
I / FoundationsI / 基礎
Foundations基礎
Before a flame burns, atoms must balance, energy must be accounted for, and reactions must be timed. Chapters 1–6 build the toolkit every later chapter draws on — thermochemistry (1–3), chemistry (4–5), and the reactor abstraction (6).火焰燃燒之前，原子必須平衡、能量必須清點、反應必須計時。第 1–6 章建立後續各章所倚賴的工具箱——熱化學（1–3）、化學（4–5），以及反應器抽象化（6）。
Stoichiometry化學計量
Fuel & Stoichiometry燃料與化學計量
Balance the atoms, supply the air, and classify any flame by equivalence ratio Φ and air–fuel ratio.平衡原子、供應空氣，並以當量比 Φ 與空燃比為任何火焰分類。
Combustion calculatorBunsen diagram
Open module →
Thermochemistry熱化學
Adiabatic Flame Temperature絕熱火焰溫度
The upper-bound temperature of any combustion process, from an enthalpy balance across reactants and products.任何燃燒過程的溫度上限，由反應物與生成物之間的焓平衡求得。
H–T diagramT_ad vs Φ
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Equilibrium平衡
Chemical Equilibrium化學平衡
At flame temperatures products dissociate. Equilibrium constants for H₂O/CO₂/O₂ dissociation, water–gas shift, and NO.在火焰溫度下生成物會解離。涵蓋 H₂O/CO₂/O₂ 解離、水煤氣轉移與 NO 的平衡常數。
K_p vs TDissociation
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Kinetics動力學
Chemical Kinetics化學動力學
The Arrhenius rate law, the H₂–O₂ chain mechanism, explosion limits, and the chemical timescale that sets ignition.阿瑞尼斯速率律、H₂–O₂ 連鎖機構、爆炸極限，以及決定點火的化學時間尺度。
Rate constantsExplosion limits
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Mechanisms機構
Reaction Mechanisms反應機構
Every fuel reduces to the same radical pool. CO + OH controls heat release; three NO routes compete with T and Φ.每種燃料最終都歸結到相同的自由基庫。CO + OH 主導放熱；三條 NO 生成路徑隨 T 與 Φ 相互競爭。
Radical poolNO routes
Open module →
Reactors反應器
Reactor Models反應器模型
Two ideal reactors bracket every real combustor. The PSR S-curve shows ignition, bistability, and blowout.兩種理想反應器框限了所有真實燃燒器。PSR 的 S 曲線呈現點火、雙穩態與吹熄。
PSR / PFRS-curve
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II / Modelling Reacting FlowsII / 反應流的建模
Modelling Reacting Flows反應流的建模
From a 0-D pot to a 3-D field. The conservation laws turn combustion into a set of PDEs (Ch. 7); turbulence is what makes those PDEs impossible to solve directly and forces every closure that follows (Ch. 8).從 0 維的容器到 3 維的場。守恆律將燃燒化為一組偏微分方程式（第 7 章）；而紊流正是使這些方程式無法直接求解、並迫使後續一切封閉模式產生的根源（第 8 章）。
Conservation laws守恆律
Governing Equations統御方程式
The exact conservation laws for reacting flows — mass, momentum, energy, species — and how Reynolds-averaging opens the closure problem.反應流的精確守恆律——質量、動量、能量、組分——以及雷諾平均如何開啟封閉問題。
Continuity → speciesClosure
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Turbulence紊流
Turbulence: A Cascade of Scales紊流：尺度的串級
Big eddies hand energy down to ever-smaller ones until viscosity rubs it away. The four length scales, the closure problem, and the self-similar jet.大渦將能量逐級傳遞給更小的渦，直到黏滯將其耗散殆盡。四個長度尺度、封閉問題，以及自相似噴流。
Energy cascadeLength scales
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III / Premixed FlamesIII / 預混火焰
Premixed Flames預混火焰
Fuel and air arrive already mixed. From the slow laminar wave at S_L ~ 1 m/s to detonations at 2 km/s, with three turbulent regimes between — one map orders them all. Chapters 9–10 cover the laminar baseline; 11–14 the turbulent regimes.燃料與空氣抵達時已混合完成。從 S_L ~ 1 m/s 的緩慢層流波，到 2 km/s 的爆轟，中間還有三種紊流區域——一張圖即可統整全部。第 9–10 章涵蓋層流基準；11–14 章為紊流區域。
Laminar baseline層流基準
Laminar Premixed Flame層流預混火焰
The flat steady 1-D flame — canonical building block of every premixed regime. S_L–Φ curves for five fuels and a flame-structure visualizer.平直穩態的一維火焰——所有預混區域的基本建構單元。五種燃料的 S_L–Φ 曲線，以及火焰結構視覺化工具。
S_L vs ΦFlame structure
Open module →
Supersonic超音速
Detonations爆轟
The supersonic cousin of a flame: a coupled shock + reaction zone at 1500–3000 m/s. Hugoniot diagram, CJ point, and ZND profile.火焰的超音速表親：以 1500–3000 m/s 行進、震波與反應區耦合的結構。Hugoniot 圖、CJ 點與 ZND 剖面。
HugoniotCJ · ZND
Open module →
Regime map · hub區域圖 · 樞紐
Flame Speed & the Regime Map火焰速度與區域圖
The hub for premixed turbulent flames: the Damköhler number, an interactive regime locator, flame-speed models, and anchoring.預混紊流火焰的樞紐：Damköhler 數、互動式區域定位器、火焰速度模型與固焰。
Borghi mapS_T models
Open module →
Ka < 1
The Wrinkled Laminar-Flame Regime皺褶層流火焰區域
The flame is thinner than the smallest eddy, so turbulence can only fold the sheet — and folding is simply added area.火焰比最小的渦還薄，因此紊流只能摺疊火焰面——而摺疊不過是增加面積。
S_T / S_L = A/A
Open module →
1 < Ka < 100
The Flamelets-in-Eddies Regime渦團中的火焰片區域
Turbulence tears large unburned pockets into smaller ones; the rate of that tearing, not the chemistry, sets the burn.紊流將大團未燃氣撕裂成較小的團塊；決定燃燒速率的是撕裂的速率，而非化學反應。
Mixing-controlled
Open module →
Ka > 100
The Distributed-Reaction Regime分佈反應區域
Even the smallest eddies stir the reacting gas itself — reaction smears across a thick, churning zone with no flame sheet left.連最小的渦也攪動反應氣體本身——反應在一個厚實、翻騰的區域中瀰漫，已不存在火焰面。
Mean of rates
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IV / Non-Premixed (Diffusion) FlamesIV / 非預混（擴散）火焰
Non-Premixed (Diffusion) Flames非預混（擴散）火焰
Now fuel must find its air. The flame lives on the surface where they meet in stoichiometric proportion. From Burke–Schumann's classic laminar flame (Ch. 15) to the lifted, blowing-out turbulent jet (Ch. 17).如今燃料必須自行尋找空氣。火焰存在於兩者以化學計量比例相遇的曲面上。從 Burke–Schumann 的經典層流火焰（第 15 章），到抬升、瀕臨吹熄的紊流噴焰（第 17 章）。
Laminar diffusion層流擴散
Laminar Diffusion Flame層流擴散火焰
No flame speed; the flame is anchored where Z = Z_st. Burke–Schumann profiles, counterflow extinction, and soot luminosity.沒有火焰速度；火焰錨定於 Z = Z_st 之處。Burke–Schumann 剖面、對衝熄滅與煤煙發光。
Burke–SchumannCounterflow
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Jet structure噴流結構
Turbulent Diffusion Flames紊流擴散火焰
A fuel jet burning into air: luminosity zones, the laminar-to-turbulent transition, the conserved scalar, and Froude-number length scaling.燃料噴流在空氣中燃燒：發光區、層流到紊流的轉變、守恆純量，以及以 Froude 數為基礎的長度尺度律。
Mixture fractionFlame length
Open module →
Stabilization穩焰
Anchoring, Lift-Off & Blowout固焰、抬升與吹熄
Push the fuel harder and the flame detaches, lifts downstream, then blows out. Soot-driven radiation and the stability window.加大燃料流量，火焰便脫離、向下游抬升，最終吹熄。由煤煙驅動的輻射與穩定窗口。
Lift-offBlowout
Open module →
✦ / Reference✦ / 參考
The governing ratios主導的比值
Combustion is largely the art of choosing the right ratio. Eight numbers — and the inequalities between them — pivot the entire course. Each card links to where it first appears.燃燒在很大程度上是選對比值的藝術。八個數字——以及它們之間的不等關係——支配著整門課程。每張卡片連結至該數首次出現之處。
Φ
Equivalence ratio當量比
Fuel/air ratio scaled to stoichiometric. Φ<1 lean, Φ>1 rich — the single mixture-strength number.以化學計量為基準縮放的燃空比。Φ<1 為貧油、Φ>1 為富油——單一的混合濃度指標。
First in Ch. 1
Re
Reynolds number雷諾數
Inertia vs viscosity. Sets the width of the cascade: ℓ_K/ℓ₀ ~ Re^−3/4.慣性對黏滯之比。決定串級的寬度：ℓ_K/ℓ₀ ~ Re^−3/4。
First in Ch. 8
Da
Damköhler numberDamköhler 數
Flow time vs chemical time. Da≫1 fast chemistry (flamelet); Da≪1 frozen.流動時間對化學時間之比。Da≫1 為快化學（火焰片）；Da≪1 為凍結。
First in Ch. 6
Ka
Karlovitz numberKarlovitz 數
Smallest-eddy time vs chemistry. Sorts the premixed regimes: <1, 1–100, >100.最小渦時間對化學時間之比。用以區分預混區域：<1、1–100、>100。
First in Ch. 11
Le
Lewis number路易士數
Thermal vs mass diffusivity. Le≠1 drives Markstein effects and cellular instabilities.熱擴散率對質量擴散率之比。Le≠1 驅動 Markstein 效應與胞狀不穩定。
First in Ch. 9
M
Mach number馬赫數
Flow vs sound speed. M≪1 for flames; M≳5 for detonations — two universes.流速對音速之比。火焰 M≪1；爆轟 M≳5——兩個截然不同的世界。
First in Ch. 10
Z
Mixture fraction混合分率
Conserved scalar for diffusion flames. The flame sits at Z = Z_st.擴散火焰的守恆純量。火焰位於 Z = Z_st。
First in Ch. 15
Frf
Flame Froude number火焰 Froude 數
Jet momentum vs buoyancy. Large Fr_f → momentum-controlled length.噴流動量對浮力之比。Fr_f 大 → 長度由動量主導。
First in Ch. 16
How to use this section. When a module says “the flame is in regime X because Ka > 100,” return here to recall which ratio that is and what it compares — each card links straight to where the number is introduced.本節用法。當某單元說「火焰處於區域 X，因為 Ka > 100」時，回到此處即可回想那是哪一個比值、它在比較什麼——每張卡片都直接連到該數首次登場之處。