## 1 Introduction  
First developed by [PERSON] [1; 2], the Eddy Dissipation Concept (EDC) model has been widely used for combustion predictions. The main idea of the EDC is that chemical reactions in turbulent flows occur in intermittent fine structures or small eddies. The species gradients and molecular mixing coexist with velocity gradients such as viscous dissipation. The EDC consists of an energy cascade model and a reactor model. The cascade model links the fine structures, where reactions are assumed to occur, to the mean turbulence field resolved by the Reynolds-averaged Navier -Stokes (RANS) equation. These smaller eddies are regarded as a reactor, and the reaction rate is formulated from the species mass balance for this reactor [1; 2; 3; 4; 5; 6]. The indisputable wide use of the EDC model indicates that the mean reaction rate is reasonably well modeled. During the last decade, various modifications have been suggested to the EDC constants, i.e., the primary EDC constants \(C_{\rm D1}\) and \(C_{\rm D2}\) or the secondary EDC constants \(C_{\rm T}\) and \(C_{\rm\gamma}\). According to the EDC model, \(C_{\rm T}\) is a function of \(C_{\rm D2}\) while \(C_{\rm\gamma}\) is a function of both \(C_{\rm D1}\) and \(C_{\rm D2}\)[5]. To the best of our knowledge, [PERSON] et al. [7] were the first to propose changing the constants for modeling high-pressure gasification processes, where \(C_{\rm T}\) up to 8 and \(C_{\rm\gamma}\) up to 13 were used. These selections varied significantly the original values, i.e., \(C_{\rm D1}=0.135\) and \(C_{\rm D2}=0.50\), while \(C_{\rm T}=0.4082\) and \(C_{\rm\gamma}=2.1298\). However, detailed effects of the modification were barely found. In addition, some misunderstandings have emerged during the use of the EDC model. For example, modified constants \(C_{\rm T}=3.0\) and \(C_{\rm\gamma}=\)2.1377 [8] were tried for the numerical investigation of turbulent natural gas combustions for jets in a coflow of lean combustion products in the Delft-Jet-in-Hot-Coflow (DJHC) burner. A numerical study of a jet-in-hot coflow (JHC) burner emulating Moderate or Intense Low-oxygen Dilution (MILD) combustion conditions was performed with modified \(C_{\tau}=1.5\) or 3.0 and \(C_{\gamma}=1.0\)[9]. A numerical study of a reversed-flow small-scale combustor was reported with modified \(C_{\gamma}=2.13\) or 5.0 [10]. A natural gas non-catalytic partial oxidation reformer was simulated with modified \(C_{\gamma}=2.14\), 3.2, 4.4, or 5.56 [11]. Lifted jet flames in a heated and depleted oxygen coflow stream were simulated with \(C_{\tau}=3.0\) and \(C_{\gamma}=0.5\), 0.75, 1.0, 1.5, or 2.5 [12]. The chemical kinetic effect of the addition of hydrogen to ethylene jet flames in a hot coflow was investigated with modified \(C_{\gamma}=3\) and \(C_{\tau}=1.0\)[13]. Biomass combustion was modeled with modified \(C_{\tau}=1.0\), 1.5, or 5.62 and \(C_{\gamma}=1.12\), 1.75, 1.8, 2.37, or 2.46 [14,15]. The gas-phase combustion of a grate-firing biomass furnace was modeled with modified constants \(C_{\tau}=1.0\), 1.5, or 5.62 and \(C_{\gamma}=1.12\), 1.75, 1.8, 2.37, or 2.46 [16]. Ethylene jet flames in diluted and heated oxidant stream combustion conditions were modeled [17] with \(C_{\tau}=3.0\) and \(C_{\gamma}=1.0\), which are the same as those used by [PERSON] et al. [8]. The Adelaide Jet in Hot Co-flow (JHC) burner at different co-flow compositions and fuel-jet Reynolds numbers was modeled with modified \(C_{\tau}=0.82\), 1.0, 1.07, 1.25, 1.47, 1.77, or 1.96 and \(C_{\gamma}=1.78\), 1.9, 2.0, or 2.14 [18]. Turbulence-chemistry interactions under hot diluted combustion of \(C_{\tau}/H_{2}\) were modeled with modified \(C_{\tau}=0.0893\), 0.2886, 0.5773, or 3.0 and \(C_{\gamma}=1.0\), 1.7976, 2.5422, or 5.795 [19]. The Adelaide Jet in Hot-Coflow burner was modeled with modified constants, \(C_{\tau}=1.47\) and \(C_{\gamma}=1.5\) or 1.9 [20], which are not the same used by [PERSON] et al. [18]. The range of validity of the values proposed for those constants is not well established.