ANALYSIS AND CORRELATIONS OF DIMENSIONLESS NUMBERS RELEVANT TO ORIFICES’ CAVITATING FLOW

Abstract

The aim of this work was to establish a general design basis for pilot-scale units to treat textile dyeing wastewater containing recalcitrant organic chemicals by hydrodynamic cavitation (HC) using orifices of various geometries. Relevant tabulated data available in the literature were analyzed and correlated to obtain universal relationships to this end. In spite of extensive effort, most of the obtained correlations were system-specific, which still can be used for design using their respective orifice geometries as demonstrated. However, one salient general relationship links the pipe’s dimensionless loss coefficient (K_LP) to the pipe’s Reynolds number (Re_P), encompassing all data under consideration, which may serve as an additional design option to optimize such units. The implication of this relationship is a lower upstream pressure (P₁) value with an increase in pipe diameter while using the same specified orifice and achieving the same desired cavitation number (C_v). The ratio of P₁ value in the larger pipe to its value in the smaller pipe is a function of the smaller pipe diameter (D_S) to the larger pipe diameter (D_L) ratio: (P₁ in D_L) / (P₁ in D_S) = (D_S /D_L)^2.33. A lower P₁ value will increase the cavitation yield by decreasing the expended energy, especially if the required number of passes is large. Additionally, the variation of the orifices’ hole loss coefficient (K_Lh) with the ratio of the holes area to the pipe cross-sectional area (A_h/A_p) for cavitating flow is compared with that for non-cavitating/incipient cavitation flow reported in the literature.

ABSTRAK: Tujuan kajian ini diadakan bagi mereka bentuk dasar umum unit skala-pandu bagi merawat pewarnaan air buangan tekstil yang mengandungi kimia organik rekalsitran daripada peronggaan hidrodinamik (HC) menggunakan orifis pelbagai geometri. Data berjadual berkaitan yang ada dalam kajian lepas dianalisa dan dikaitkan bagi mendapatkan kaitan universal hingga akhir. Walaupun pelbagai usaha telah dijalankan, banyak kaitan didapati mengguna pakai sistem-tertentu, di mana boleh digunakan bagi mereka cipta menggunakan geometri orifis yang ditunjukkan. Walau bagaimanapun, bagi menghubung kait pekali langsung tanpa dimensi (K_LP) kepada paip nombor Reynolds (Re_P), meliputi semua data di bawah pertimbangan, di mana membantu pilihan rekaan tambahan bagi mengoptimum unit tersebut. Implikasi hubungan ini adalah nilai tekanan hulu sungai bawah (P₁) dengan penambahan diameter paip dengan menggunakan orifis sama yang sebenar dan mendapati nombor peronggaan yang sama diingini (C_v). Nisbah nilai P₁ dalam paip besar kepada nilai paip kecil adalah berkadaran pada nisbah diameter paip kecil (D_S) kepada diameter paip besar (D_L):  

(P₁ dalam D_L) / (P₁ in D_S) = (D_S /D_L)^2.33.