基于Driscoll凹腔稳焰模型的超声速燃烧火焰稳定尺度效应研究

Scaling Effect of Supersonic Combustion Flame Stabilization Based on Driscoll Cavity Blowout Limits Model

为了研究超声速燃烧室尺度放大后,保持火焰稳定边界相对于基准燃烧室不变,凹腔火焰稳定器几何参数应遵循何种放大准则的问题,基于已有的Driscoll凹腔稳焰数学模型,采用典型的单凹腔矩形截面燃烧室作为基准燃烧室,分别计算基准燃烧室在贫燃和富燃状态时的火焰稳定准则数DaNP,再按照燃烧室尺度放大定义写出尺度放大燃烧室的稳焰准则数表达式Da′NP,将稳焰边界不变作为约束条件,构建尺度放大准则方程式DaNP=Da′NP,求解准则方程式获得凹腔几何参数放大准则表达式,绘制准则特性曲线,分析归纳近似准则,并通过数值计算方法初步验证准则的有效性。采用Driscoll凹腔稳焰模型的尺度效应分析结果表明,燃烧室放大一定倍数n后,无法通过调整凹腔长度和深度放大倍数k1和k2使得贫燃熄火边界保持不变;但是,可以通过调整参数k1和k2使得富燃熄火边界保持不变,此时凹腔几何参数遵循的放大准则近似为k 1≈k 2≈n^(1/4)。

In order to investigate the magnifying rule of cavity flameholder,theoretic and numerical studies were conducted on the scaled supersonic combustor under the condition of the constant flame blowout limits.First,based on the Driscoll cavity blowout limits model including lean and rich blowout limits embranchment model,a typical rectangular section combustor with single-cavity was employed as the benchmark combustor to calculate flame stabilization Damkohler number DaNP.Secondly,according to the definition of scaling effect of combustor,flame stabilization Damkohler number Da′NP expression of the scaled combustor was derived.Thirdly,by keeping the flame blowout limits constant,the equation DaNP=Da′NPwas deduced.By solving the above equa⁃tion,the magnifying rule expression of cavity flameholder was acquired,and the characteristic curves of scaling effect were drawn.The approximate magnifying rule was obtained by means of analyzing the curves.Finally,the availability of the rule was demonstrated elementarily by numerical simulation.The research results show that the flame lean blowout limit could not be kept constant through adjusting scaling coefficient k1 and k2 of cavity length and cavity depth when a combustor is scaled to be n of the benchmark combustor,however,the flame rich blowout limit could keep constant through adjusting scaling coefficient k1 and k2 of cavity length and cavity depth when a combustor is scaled to be n of the benchmark combustor,the approximate magnifying rule is k 1≈k 2≈n^(1/4).