Characteristics of the transition from supercritical to subcritical regime (hydraulic jump) in laminar flow of a Herschel-Bulkley fluid on an horizontal plane are examined. The set of equations governing the flow is presented, recovering earlier results for a Bingham fluid. The determination of the flow conditions downstream, given those upstream, involves solution of a nonlinear algebraic system in three unknowns; an approximate analytical formula for conjugate depths is derived since no exact solution can be obtained in closed form. The relative error thus introduced is then evaluated numerically; its maximum value is shown to be less than a few percent. The behavior of flow depth, bottom shear stress and critical depth are established and illustrated as function of the flow behavior index; the critical depth and the ratio of conjugate depths increase with the behavior index and until the bottom shear stress exceeds a certain value, and then decrease afterwards.
Transition from supercritical to subcritical regime in free surface flow of yield stress fluids / R. Ugarelli; V. Di Federico. - In: GEOPHYSICAL RESEARCH LETTERS. - ISSN 0094-8276. - STAMPA. - 34:(2007), pp. L21402-doi:10.1029.... [10.1029/2007GL031487]
Transition from supercritical to subcritical regime in free surface flow of yield stress fluids
UGARELLI, RITA MARIA;DI FEDERICO, VITTORIO
2007
Abstract
Characteristics of the transition from supercritical to subcritical regime (hydraulic jump) in laminar flow of a Herschel-Bulkley fluid on an horizontal plane are examined. The set of equations governing the flow is presented, recovering earlier results for a Bingham fluid. The determination of the flow conditions downstream, given those upstream, involves solution of a nonlinear algebraic system in three unknowns; an approximate analytical formula for conjugate depths is derived since no exact solution can be obtained in closed form. The relative error thus introduced is then evaluated numerically; its maximum value is shown to be less than a few percent. The behavior of flow depth, bottom shear stress and critical depth are established and illustrated as function of the flow behavior index; the critical depth and the ratio of conjugate depths increase with the behavior index and until the bottom shear stress exceeds a certain value, and then decrease afterwards.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.