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Cheng-lung Chen

Publications and source records attributed to Cheng-lung Chen.

18 recordsLinked to original sources
USGS1997

Resistance formulas in hydraulics-based models for routing debris flows

The one-dimensional, cross-section-averaged flow equations formulated for routing debris flows down a narrow valley are identical to those for clear-water flow, except for the differences in the values of the flow parameters, such as the momentum (or energy) correction factor, resistance coefficient, and friction slope. Though these flow parameters for debris flow in channels with cross-sections of arbitrary geometric shape can only be determined empirically, the theoretical values of such parameters for debris flow in wide channels exist. This paper aims to derive the theoretical resistance coefficient and friction slope for debris flow in wide channels using a rheological model for highly-concentrated, rapidly-sheared granular flows, such as the generalized viscoplastic fluid (GVF) model. Formulating such resistance coefficient or friction slope is equivalent to developing a generally applicable resistance formula for routing debris flows. Inclusion of a nonuniform term in the expression of the resistance formula proves useful in removing the customary assumption that the spatially varied resistance at any section is equal to what would take place with the same rate of flow passing the same section under conditions of uniformity. This in effect implies an improvement in the accuracy of unsteady debris-flow computation.

Conference Paper↗
USGS1993

Unique laminar-flow stability limit based shallow-water theory

Two approaches are generally taken in deriving the stability limit for the Froude number (𝐹𝑠) for laminar sheet flow: The first approach uses the Orr‐Sommerfeld equation, while the second uses the cross‐section‐averaged equations of continuity and motion. Because both approaches are based on shallow‐water theory, the values of 𝐹 𝑠 obtained from both approaches should be identical, yet in the literature they are not. This suggests that a defect exists in at least one of the two approaches. After examining the governing equations used in both approaches, one finds that the existing cross‐section‐averaged equation of motion is dependent on the frame of reference. To correct this defect, one can formulate a frame‐independent equation of motion relative to a coordinate system moving with constant velocity, then derive a new expression for 𝐹 𝑠 that is generally applicable to both laminar and turbulent flows in prismatic channels of arbitrary cross‐sectional geometry. For laminar sheet flow, the new expression for 𝐹 𝑠 obtained from the second approach yields 𝐹 𝑠 ≃0.527 , which agrees with that obtained from the first approach.

Journal of Hydraulic Engineering↗
USGS1993

Continuum-mechanics-based rheological formulation for debris flow

This paper aims to assess the validity of the generalized viscoplastic fluid (GVF) model in the light of both the classical relative-viscosity versus concentration relation and the dimensionless stress versus shear-rate squared relations based on kinetic theory, thereby addressing how to evaluate the rheological parameters of the GVF model using Bagnold's data.

Conference Paper↗
USGS1992

Momentum and energy coefficients based on power-law velocity profile

The theoretical momentum coefficient (β) and energy coefficient (α) for turbulent shear flow in circular pipes and wide channels are derived from the power law, then compared with their counterparts on the basis of the logarithmic law. For such unidirectional flows, the exponent (m) of the power‐law velocity distribution is the sole parameter that determines the values of β and α. A comparison of the corresponding expressions for β and α derived using both laws shows that their values differ only slightly within a valid range of small m's. Use of a power‐law‐based β expression along with a power‐law resistance formula in the cross‐section‐averaged equation of momentum cannot only eliminate the theoretical incompatibility that results from mixing logarithmic and power laws in the equation but also remove the inconsistent assumption of β = 1 "> β = 1 made in the equation. Improvement on the accuracy of the flow computation by incorporating a power‐law‐based p expression in the equation of momentum is demonstrated through an example in which a new stability limit for the Froude number for turbulent shear flow in wide channels can be accurately derived without assuming β = 1 . "> β = 1 .

Journal of Hydraulic Engineering↗
USGS1992

Numerical simulation of a sphere moving down an incline with identical spheres placed equally apart

This paper describes a numerical study of an elastic sphere moving down an incline with a string of identical spheres placed equally apart. Two momentum equations and a moment equation formulated for the moving sphere are solved numerically for the instantaneous velocity of the moving sphere on an incline with different angles of inclination. Input parameters for numerical simulation include the properties of the sphere (the radius, density, Poison's ratio, and Young's Modulus of elasticity), the coefficient of friction between the spheres, and a damping coefficient of the spheres during collision.

Conference Paper↗
USGS1991

Unified theory on power laws for flow resistance

Two general power formulas, one for hydraulically smooth flows and the other for fully rough flows, are derived in a rational way from the widely accepted logarithmic formulas for the velocity profile and the Darcy‐Weisbach friction factor. A regression analysis based on the method of least squares is used to determine the valid range of the local velocity (or normal distance from the wall) in the power formula. Some older empirical formulas, such as Lacey's, Manning's, Blasius', and Hazen‐Williams', and their valid ranges, are actually explained analytically by the results. Incomplete self‐similarity of the power law, in which the exponent and the associated coefficient vary with the similarity parameters, such as the Reynolds number and the relative roughness, is elucidated through the parametric representations of the power formulas and their counterparts based on the logarithmic law. This paper examines the concept and rationale behind the power formulation of uniform turbulent shear flows, thereby addressing some critical issues in the modeling of flow resistance based on the power law.

Journal of Hydraulic Engineering↗
USGS1990

Rheological properties of simulated debris flows in the laboratory environment

Steady debris flows with or without a snout are simulated in a 'conveyor-belt' flume using dry glass spheres of a uniform size, 5 or 14 mm in diameter, and their rheological properties described quantitatively in constants in a generalized viscoplastic fluid (GVF) model. Close agreement of the measured velocity profiles with the theoretical ones obtained from the GVF model strongly supports the validity of a GVF model based on the continuum-mechanics approach. Further comparisons of the measured and theoretical velocity profiles along with empirical relations among the shear stress, the normal stress, and the shear rate developed from the 'ring-shear' apparatus determine the values of the rheological parameters in the GVF model, namely the flow-behavior index, the consistency index, and the cross-consistency index. Critical issues in the evaluation of such rheological parameters using the conveyor-belt flume and the ring-shear apparatus are thus addressed in this study.

Conference Paper↗
USGS1989

Idealized debris flow in flume with bed driven by a conveyor belt

The generalized viscoplastic fluid (GVF) model is used to derive the theoretical expressions of two-dimensional velocities and surface profile for debris flow established in a flume with bed driven by a conveyor belt. The rheological parameters of the GVF model are evaluated through the comparison of theoretical results with measured data. A slip velocity of the established (steady) nonuniform flow on the moving bed (i.e., the conveyor belt) is observed, and a relation between the slip velocity and the velocity gradient at the bed is derived. Two belts, one rough and the other smooth, were tested. The flow profile in the flume is found to be linear and dependent on the roughness of the belt, but not much on its speed.

Conference Paper↗
USGS1988

Generalized viscoplastic modeling of debris flow

Various concepts have been proposed or used in the development of Theological models for debris flow. The earliest model developed by Bagnold was based on the concept of the “dispersive” pressure generated by grain collisions. Bagnold's concept appears to be theoretically sound, but his empirical model has been found to be inconsistent with most theoretical models developed from non‐Newtonian fluid mechanics. Although the generality of Bagnold's model is still at issue, debris‐flow modelers in Japan have generally accepted Takahashi's formulas derived from Bagnold's model. Some efforts have recently been made by theoreticians in non‐Newtonian fluid mechanics to modify or improve Bagnold's concept or model. A viable rheological model should consist both of a rate‐independent part and a ratedependent part. A generalized viscoplastic fluid (GVF) model that has both parts as well as two major rheological properties (i.e., the normal stress effect and soil yield criterion) is shown to be sufficiently accurate, yet practical, for general use in debris‐flow modeling. In fact, Bagnold's model is found to be only a particular case of the GVF model. Analytical solutions for (steady) uniform debris flows in wide channels are obtained from the GVF model based on Bagnold's simplified assumption of constant grain concentration.

Journal of Hydraulic Engineering↗
USGS1988

General solutions For viscoplastic debris flow

Theoretical velocity profile and theoretical pressure and concentration distributions for (steady) uniform debris flow in wide channels are derived from a generalized viscoplastic fluid (GVF) model without imposing R. A. Bagnold's assumption of constant grain concentration. Good agreement between the theoretical velocity profile and the experimental data of Japanese scientists strongly supports the validity of both the GVF model and the proposed method of solution from the model. It is shown that both E. C. Bingham and Bagnold versions (or submodels) of the GVF model can be used to simulate debris flow at the dynamic state. Although Bagnold's dilatant submodel appears to fit the Japanese data better than the Bingham submodel for flow of noncohesive grains, the choice between them is by no means clear-cut.

Journal of Hydraulic Engineering↗
USGS1988

Power formula for open-channel flow resistance

This paper evaluates various power formulas for flow resistance in open channels. Unlike the logarithmic resistance equation that can be theoretically derived either from Prandtl's mixing-length hypothesis or von Karman's similarity hypothesis, the power formula has long had an appearance of empiricism. Nevertheless, the simplicity in the form of the power formula has made it popular among the many possible forms of flow resistance formulas. This paper reexamines the concept and rationale of the power formulation, thereby addressing some critical issues in the modeling of flow resistance.

Conference Paper↗
USGS1987

DISCHARGE AND DEPTH BEHIND A PARTIALLY BREACHED DAM.

The role that the velocity-distribution correction factor plays in the determination of the flood discharge and corresponding flow depth behind a partially breached dam is investigated. Assumption of a uniformly progressive flow for an established dam-break flood in a rectangular channel of infinite extent leads to the formulation of a theoretical relation between the depth and velocity of flow expressed in differential form. Integrating this ordinary differential equation, one can express the velocity in terms of the depth.

Conference Paper↗
USGS1986

VISCOPLASTIC FLUID MODEL FOR DEBRIS FLOW ROUTING.

This paper describes how a generalized viscoplastic fluid model, which was developed based on non-Newtonian fluid mechanics, can be successfully applied to routing a debris flow down a channel. The one-dimensional dynamic equations developed for unsteady clear-water flow can be used for debris flow routing if the flow parameters, such as the momentum (or energy) correction factor and the resistance coefficient, can be accurately evaluated. The writer's generalized viscoplastic fluid model can be used to express such flow parameters in terms of the rheological parameters for debris flow in wide channels. A preliminary analysis of the theoretical solutions reveals the importance of the flow behavior index and the so-called modified Froude number for uniformly progressive flow in snout profile modeling.

Conference Paper↗
USGS1985

PRESENT STATUS OF RESEARCH IN DEBRIS FLOW MODELING.

A viable rheological model should consist of both a time-independent part and a time-dependent part. A generalized viscoplastic fluid model that has both parts as well as two major rheological properties (i. e. , the normal stress effect and soil yield criteria) is shown to be sufficiently accurate, yet practical, for general use in debris flow modeling. Other rheological models, such as the Bingham plastic fluid model and the so-called Coulomb-viscous model, are compared in terms of the generalized viscoplastic fluid model.

Conference Paper↗
USGS1979

Field verification of reconstructed dam-break flood, Laurel Run, Pennsylvania

A one-dimensional dam-break flood routing model is verified by using observed data on the flash flood resulting from the failure of Laurel Run Reservoir Dam near Johnstown, Pennsylvania. The model has been developed on the basis of an explicit scheme of the characteristics method with specified time intervals. The model combines one of the characteristic equations with the Rankine-Hugoniot shock equations to trace the corresponding characteristic backward to the known state for solving the depth and velocity of flow at the wave front. The previous version of the model has called for a modification of the method of solution to overcome the computational difficulty at the narrow breach and at any geomorphological constraints where channel geometry changes rapidly. The large reduction in the computational inaccuracies and oscillations was achieved by introducing the actual "storage width" in the equation of continuity and the imaginary "conveyance width" in the equation of motion. Close agreement between observed and computed peak stages at several stations downstream of the dam strongly suggests the validity and applicability of the model. However, small numerical noise appearing in the computed stage and discharge hydrographs at the dam site as well as discrepancy of attenuated peaks in the discharge hydrographs indicate the need for further model improvement.

Pennsylvania↗