CN111931429A - Simulation method for change of effective density of flocs along with particle size - Google Patents

Abstract

The invention provides a method for simulating the change of effective density of flocs along with particle size, which considers the influence of turbulent shear rate on the structure of the formed flocs and provides a characteristic fractal dimension F of the flocs_cAnd improving the effective density simulation method of the flocs according to the functional relation between the water body turbulent shear rate G. The invention not only considers the influence caused by the change of the particle size of the floc but also innovatively introduces the influence of the environmental factor of the water body turbulent shear rate when simulating and calculating the effective density of the floc, thereby solving the defect that the traditional simulation method is only suitable for a certain specific water body turbulent shear environment and is difficult to fully reflect the change characteristics of the effective density of the floc under the conditions of water power and water body turbulent shear variation in natural conditions. The simulation method can enlarge the application range of the effective density simulation of the flocs, effectively improve the simulation precision of the effective density of the flocs under different water body turbulent fluctuation conditions, and lay a solid foundation for accurately predicting the transportation and transfer of the fine-particle silt and the pollutants carried by the fine-particle silt.

Description

Simulation method for change of effective density of flocs along with particle size

Technical Field

The invention relates to the field of sediment motion mechanics, in particular to a simulation method for the change of effective density of flocs along with particle size.

Background

The flocculation property is a main mark for distinguishing the sticky sediment from the non-sticky sediment and is also a key point and a difficult point for researching the basic theory and the movement law of the sticky sediment. The non-sticky silt mainly moves in single particles, the sticky silt is subjected to flocculation, the particles are bonded with each other to form aggregates with increased particle size, the aggregates are called floccules, and most of the sticky silt is transported in the floccules in natural water. The settling velocity is the most important factor for controlling and predicting the transport and deposition process of silt in the water body and is mainly controlled by the particle size and the effective density of flocs. The particle size of the flocs can be generally obtained through observation, and a simulation method for the particle size change of the flocs is relatively mature, but the research and the knowledge on the effective density of the flocs are relatively weak, so that the key point for the simulation success or failure of the key parameter of the sedimentation speed of the flocs lies in the simulation of the effective density of the flocs. There are two main methods for simulating the change of effective density of flocs with the particle size.

First of allThe simulation method is based on self-similar fractal theory, and Kranenburg (1994) proposes to utilize fractal dimension N_fDescribing the relationship between effective floc density Δ ρ and particle size D as:

where rho_fAnd ρ_wRespectively the flock density and the density of water (typically 1000kg m)^-3)，ρ_pThe density of dispersed particles constituting the flocs (generally 2650kg m)^-3). In this simulation method, the fractal dimension N of the floc masses_fIs a constant which does not vary with the flock size and is usually taken to be 2.

The second simulation method is based on the study that the fractal dimension of the flocs changes with the particle size. Khelifa and Hill (2006) (i.e. Khelifa, A., Hill, P.S.,2006 model for effective density and setting level of flocs. J.Hydraul. Res.44, 390-401. doi:10.1080/00221686.2006.9521690) suggests that the fractal dimension of the silt particles in the original dispersion state is 3, and the fractal dimension of the flocs decreases in a power function manner along with the increase of the particle size along with the aggregation of the particles and the development of the flocs, so that the relationship between the effective density Δ ρ of the flocs and the particle size D is as follows:

N_f＝3(D/d)^β,β＝[log(F_c/3)]/[log(D_fc/d)]

in the formula D_fcIs a characteristic floc grain diameter, and the corresponding fractal dimension is F_c。

The inventor of the application finds out through research in the process of implementing the invention that: the first simulation method only introduces the fractal structure of the floc, but does not consider that the fractal dimension for representing the fractal structure of the floc changes; the second simulation method considers the characteristic that the fractal dimension of the flocs is reduced along with the increase of the particle size on the basis of the first method, but does not consider the key factor that the fractal dimension of the flocs is obviously different due to different flocculation environments, particularly the turbulent shear rate of water, which influences flocculation. Therefore, both current main methods are difficult to better simulate the effective density of the flocs, especially in the environment where the turbulent shear of the water body changes significantly.

Disclosure of Invention

Aiming at the defects in the prior art, the invention provides a simulation method for the change of the effective density of the floc aggregates along with the particle size, so as to realize better simulation of the effective density of the floc aggregates.

A simulation method for the variation of effective density of flocs with particle size features that the influence of turbulent shear rate on the structure of flocs is considered and the characteristic fractal dimension F of flocs is presented_cAnd improving the floc effective density simulation method through the functional relation between the floc effective density and the water body turbulent shear rate G, which comprises the following steps:

N_f＝3(D/d)^β,β＝[log(F_c/3)]/[log(D_fc/d)]

F_c＝N_fte^kG

in the formula: Δ ρ is the effective density of the flocs, ρ_pDensity of dispersed particles, rho, to form flocks_wIs the density of water, D is the floc particle size, D is the median particle size of the dispersed silt, N_fFractal dimension of floc, D_fcIs a characteristic floc particle size, N_ftCharacteristic fractal dimension F of floc under still water condition (G ═ 0)_cK is a constant and is obtained by observation and calibration, and G is the turbulent shear rate of the water body.

The invention not only considers the influence caused by the change of the particle size of the floc but also innovatively introduces the influence of the environmental element of the turbulent shearing rate of the water body when simulating and calculating the effective density of the floc, thereby solving the defect that the traditional simulation method is only suitable for a certain specific turbulent shearing environment and is difficult to fully reflect the change characteristic of the effective density of the floc under the condition of variable turbulent shearing of the water body under natural conditions. The simulation method can enlarge the application range of the effective density simulation of the flocs, effectively improve the simulation precision of the effective density of the flocs under different water body turbulent fluctuation conditions, and lay a solid foundation for accurately predicting the transportation and transfer of the fine-particle silt and the pollutants carried by the fine-particle silt.

Drawings

FIG. 1 shows the turbulent shear rate of water body of 50s^-1And 65^-1A corresponding relation graph of effective density and particle size of flocs obtained by testing in a 7 per mill saline environment under the condition;

FIG. 2 shows the turbulent shear rate of water body at 30s^-1And 40^-1A corresponding relation graph of effective density and particle size of flocs obtained by testing in a 7 per mill saline environment under the condition;

FIG. 3 shows the turbulent shear rate of water body is 10s^-1And 20^-1A corresponding relation graph of effective density and particle size of flocs obtained by testing in a 7 per mill saline environment under the condition;

FIG. 4 is a characteristic fractal dimension F of a floc of the invention_cFitting the corresponding relation with the turbulent shear rate;

FIG. 5 is a comparison of the effective densities of the flocks from the three simulations.

Detailed Description

The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings.

On the basis of the conventional Khella and Hill (2006) simulation method, the invention considers the influence of the turbulent shear rate on the formed floc structure and provides a characteristic fractal dimension F of the floc_cAnd a functional relation with the water body turbulent shear rate G, and an improved floc effective density simulation method specifically comprises the following steps:

N_f＝3(D/d)^β,β＝[log(F_c/3)]/[log(D_fc/d)]

F_c＝N_fte^kG

in the formula: Δ ρ is the effective density of the flocs, ρ_pDensity of dispersed particles, rho, to form flocks_wIs the density of water, D is the floc particle size, D is the median particle size of the dispersed silt, N_fFractal dimension of floc, D_fcIs a characteristic floc particle size, N_ftCharacteristic fractal dimension F of floc under still water condition (G ═ 0)_cK is a constant and is obtained by observation and calibration, and G is the turbulent shear rate of the water body.

(1) According to the measured data, determining the feature fractal dimension F of the flocs under different turbulent shear rates by adopting a Khelifa and Hill (2006) simulation method_c. FIGS. 1-3 show that the turbulent shear rate of the water body is 50s^-1And 65^-1、30s^-1And 40^-1And 10s^-1And 20^-1The corresponding relation diagram of effective density and particle size of the floc obtained by testing in a 7 per mill saline environment under the condition. Best fit F obtained using the Khelifa and Hill (2006) simulation method_cAre 2.1, 1.8 and 1.6 (D), respectively_fc＝200μm，d＝11.7μm)。

(2) Determining F based on the fitting result of the fractal dimension of the optimal floc characteristics under different turbulent shear rates_c＝N_fte^kGParameter N in the relation_ftAnd the value of k (as shown in figure 4). The water body turbulence shear rate G is the average value of two water body turbulence shear rates in the test, for example, the water body turbulence shear rate is 50s^-1And 65^-1The group G was 57.5s^-1Obtaining N in the characteristic flocculation environment_ft＝1.45，k＝0.006。

(3) And (3) verifying the simulation improvement effect: the effective density of The flocs obtained under The condition of 6 groups of turbulent shear rates is simulated by using a Kranenburg (1994) method (namely Kranenburg, C.,1994, The fractional structure of The synergistic section aggregates, Estuar, coast, Shelf Sci.39, 451-460. doi:10.1016/S0272-7714(06)80002-8), a Khellifa and Hill (2006) method and The improved method provided by The invention, and The Root Mean Square Error (RMSE) of The simulation result of each method is calculated as shown in FIG. 5. The results showed that the RMSE obtained by the method of Kranenburg (1994) was the largest and 308 (N)_f2), the RMSE obtained by the method of Khella and Hill (2006) is 268 (i.e. ((ii))F_c2) RMSE of 231 (N) is obtained by the improved process of the invention_ft1.45, k 0.006), which are respectively reduced by 25% and 14% compared with the former two methods, is obviously superior to the existing simulation method of effective density of the flocs.

The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (1)

1. A simulation method for the change of effective density of flocs along with the particle size is characterized in that: considering the influence of the turbulent shear rate on the structure of the formed floc, the characteristic fractal dimension F of the floc is provided_cAnd improving the floc effective density simulation method through the functional relation between the floc effective density and the water body turbulent shear rate G, which comprises the following steps:

N_f＝3(D/d)^β，β＝[log(F_c/3)]/[log(D_fc/d)]

F_c＝N_fte^kG

in the formula: Δ ρ is the effective density of the flocs, ρ_pDensity of dispersed particles, rho, to form flocks_wIs the density of water, D is the floc particle size, D is the median particle size of the dispersed silt, N_fFractal dimension of floc, D_fcIs a characteristic floc particle size, N_ftCharacteristic fractal dimension F of floc under still water condition (G ═ 0)_cK is a constant and is obtained by observation and calibration, and G is the turbulent shear rate of the water body.

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