CN116822402A - Turbulent flow field and suspended sediment concentration field simulation method under grid disturbance - Google Patents
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Abstract
The application relates to a turbulence field and suspended sediment concentration field simulation method under grid disturbance, which comprises the steps of determining a turbulence model control equation based on a level set double-fluid space filtering large vortex simulation (LES) model, establishing a level set model, tracking fluctuation of a free water surface by using a level set function method, setting the density and viscosity of the whole calculation domain as constant values, reconstructing the above formula into a single fluid equation, solving the level set convection equation, integrating a viscous sediment model into a SCHISM simulation system, adopting an SCB model in a fine particle sediment flocculation sedimentation process, adopting a immersed boundary method to treat a fluid-solid coupling problem, adopting a split-step method to solve a fluid equation, improving calculation efficiency by MPI parallelization, and finally solving so as to simulate and output a turbulence field and a suspended sediment concentration field under grid disturbance. According to the application, the fine-particle sediment flocculation sedimentation group model and the viscous sand model are added on the basis of the SCHISM model, so that a turbulence field and a suspended sediment concentration field under grid disturbance can be effectively simulated.
Description
Technical Field
The application belongs to the technical field of hydraulic engineering experiments, and particularly relates to a simulation method of a turbulence field and a suspended sediment concentration field under grid disturbance.
Background
Grid turbulence, commonly referred to as near-isotropic turbulence, is the basis for studying complex turbulence and related material transport. The method for generating the grating turbulence in the laboratory comprises a fixed grating method and a vibrating grating method. The fixed grid method is not easy to control, has quicker attenuation and can be used for short observation time. The vibrating grating method is characterized in that a single-piece or multi-piece grating vibrates in a direction perpendicular to the plane of the grating in a water tank, jet flow and wake flow are respectively generated at the opening and the connection position of the grating, and after the jet flow and the wake flow are mixed with each other, an approximately isotropic turbulence is generated at a certain distance from the grating, which is called vibrating grating turbulence (Oscillating Grid Turbulence, OGT). The characteristics of the OGT are easily controlled by changing the operating parameters of the grating, including grating aperture size, amplitude and frequency, etc., and can be maintained for a longer period of time without attenuation, facilitating the implementation of measurements and being widely used.
The start and suspension of sediment in nature are sometimes caused by high-intensity turbulence rather than average flow, and grid turbulence can effectively simulate sediment movement under such special water flow conditions. In addition, the turbulence of the grid can separate the turbulence effect to study turbulent diffusion of sediment and pollutants, adsorption and desorption of sediment to inorganic matters and the like. Therefore, although the generation mechanism of the indoor vibration grating turbulence is different from that of the natural turbulence, the indoor vibration grating turbulence is widely applied to research on movement of sediment, pollutants and the like. By utilizing OGT, rouse first researches the sediment suspension characteristic and obtains a well-known Rouse suspended matter vertical distribution formula, and other domestic and foreign scholars research and obtain the key mechanisms of sediment transport such as sediment starting rule, relation of sediment diffusion coefficient and momentum exchange coefficient. However, the conventional grid turbulence systems often employ vertical vibrating grids, which create turbulence that is different than natural. In addition, the prior vibrating grating has smaller scale, generally tens of centimeters, and the grating is single-piece or double-piece, so that a plurality of the vibrating gratings have been studied freshly.
Disclosure of Invention
The embodiment of the application aims to provide a method for simulating a turbulence field and a suspended sediment concentration field under grid disturbance, which can effectively simulate the turbulence field and the suspended sediment concentration field under grid disturbance.
In order to achieve the above purpose, the present application provides the following technical solutions:
a method for simulating a turbulence field and a suspended sediment concentration field under grid disturbance comprises the following specific steps:
s1, establishing a fluid control equation of a large vortex model of double-fluid space filtration based on a level set equation;
s2, establishing a level set model in the model, and tracking the fluctuation of the free water surface by using a level set function method;
s3, classifying and describing flocculation polymerization and splitting processes based on the size of sediment particles in a model;
s4, treating the solid-liquid two phases in the model by using an immersed boundary method;
s5, solving a model control equation by adopting a split step method;
s6, simulating a turbulent flow field and a suspended mass sediment concentration field under the disturbance of the output grid.
The step S1 is a specific step of establishing a fluid control equation of a large vortex model of double-fluid space filtration based on a level set equation, and the specific step is as follows:
and constructing a turbulence model control equation by using a large vortex simulation model of double-fluid space filtration based on a level set:
wherein phi is a defined level set function; zeta type toy i In the form of a grid of coordinates,is a conversion matrix; j is the Jacobian matrix of the conversion matrix; u (U) i To control the flux of the body; u (u) i Is the flow rate component; ρ is the density; μ is the dynamic viscosity coefficient; p is the pressure, τ li Is the compressive lattice stress tensor; kappa is the surface curvature; delta ij Is a Kronecker trigonometric function; h is a smooth Heaviside function; re, fr and We are the non-dimensional Reynolds number, froud, respectivelye and Weber numbers are defined as follows:
wherein U and L are respectively a characteristic flow rate and a characteristic length; g is gravity acceleration; ρ water Sum mu water The density and viscosity coefficient of water respectively; σ is the surface tension.
The specific steps of the step S2 are as follows:
s21, the level set function phi is a signed distance function, the water phase is positive, the air phase is negative, the density and viscosity in each phase are constant values, the transition is smooth near the crossing interface and varies along with the distance 2 epsilon, the density and viscosity in the water phase and the air phase are calculated by using the level set function phi,
ρ(φ)＝ρ air +(ρ water -ρ air )h(φ)
μ(φ)＝μ air +(μ water -μ air )h(φ)
h (φ) is a smooth Heaviside function defined as follows:
s22, the free water surface is a set with a distance function phi of zero, and a level set equation is solved to obtain:
s23, after solving the level set convection equation, the distance function is not guaranteed to be a unit gradient, the conservation of mass of two phases is guaranteed, and in order to solve the problem of non-conservation, the model solves the mass conservation constant weight initialization equation.
The specific steps of the step S3 are as follows:
s31, dividing the flocculation group into N discrete groups, and using the parting dimension N f Description of ith flocculationFractal characteristics of the group:
wherein m is i ，D i ，ρ f,i Respectively representing the mass, diameter and density of the ith flocculation group, D p Is the major particle diameter;
s32, each flocculation group corresponds to a representative size, and the grouping size is the main particle diameter D p To the maximum floc size D max Logarithmic distribution between the flocculation groups according to the size range [ D ] min ，D max ]Automatically adjusting;
s33, sediment particle exchange among flocculation groups adopts a double-body interaction mode, is controlled by aggregation, shearing crushing and collision crushing of flocculation groups, and causes the capture and loss of sediment particles, and the general equation is as follows:
wherein n is k The number (m-3) of sediment particles in the kth group of flocculation groups; g aggr And L aggr The sediment particle capturing and losing number (m-3) caused by the flocculation polymerization; g break-shear And L break-shear The sediment particle capturing and losing number (m-3) caused by shearing and crushing respectively; g break-call And L break-call The number (m-3) of sediment particle capturing and losing caused by collision and breaking of the flocculation.
5. The method for simulating the turbulence field and the suspended sediment concentration field under the disturbance of the grid according to claim 1, wherein the specific implementation step of the step S4 is as follows:
s41, taking the grid as a solid and taking the water body in the water tank as a fluid in an intrusion boundary method; the aperture ratio of the grid meets the condition of generating turbulence similar to isotropy, and the local encryption grid can reflect the shape and the spacing of local grid holes;
s42, simulating an approximately isotropic turbulence field generated by grid oscillation by using an LES method, wherein the grid moves in a sine function mode in the transverse direction:
L＝A·sin(f·2nt)
wherein A is amplitude, f is vibration frequency, t is time, and L is grid position;
s43, various working conditions of a physical model test can be generated by adjusting the vibration frequency and amplitude of the grid so as to realize effective simulation of a turbulence field and a suspended mass sediment concentration field under grid disturbance.
The specific implementation steps of the step S5 are as follows:
s51, solving a fluid control equation by adopting a split-step method, wherein a momentum equation adopts a 2-order precision central differential format discrete space-time term comprising viscosity, pressure gradient and SGS term, adopts a 3-order precision WENO format or a 2-order central differential format discrete convection term, and adopts a 2-order precision Crank-Nicholson format to perform time propulsion:
where n represents the previous time step, Δt is the time step, F is the right hand term excluding the pressure term in the 2 nd control equation in step S1, and P is the pressure term.
S52, applying a continuity condition at the 2 nd stage of the splitting step by adopting a 3-point center differential format, and solving the following poisson pressure equation:
where n is a pressure correction term used to update the pressure and velocity fields calculated in step 1 of the splitting step:
p n+1 ＝p n +Π
the specific implementation steps of the step S6 are as follows:
s61, setting initial conditions and boundary conditions of a mathematical model, wherein the initial conditions are set to turbulent flow velocity and suspended sediment concentration, and the boundary conditions are set to be periodic boundaries.
S62, operating the model, and outputting a turbulent flow field and a suspended solid sediment concentration field under the simulated grid disturbance.
Compared with the prior art, the application has the beneficial effects that:
according to the simulation method for the turbulent flow field and the suspended sediment concentration field under grid disturbance, provided by the application, the fine particle sediment flocculation sedimentation group model and the viscous sand model are added on the basis of the SCHISM model, the viscous sediment model is integrated into the SCHISM simulation system, the fluid-solid coupling problem is simulated by adopting the submerged boundary method to solve, and the turbulent flow field and the suspended sediment concentration field under grid disturbance can be effectively simulated.
Drawings
FIG. 1 is a schematic flow chart of the method of the present application.
FIG. 2 schematic representation of SCB model of flocculation polymerization and disruption.
FIG. 3 is a schematic view of a discrete grid of tank bodies and vibrating gratings.
Fig. 4 is a partial grid schematic of a transverse vibrating grid.
Fig. 5 is a schematic diagram of vibration frequency and amplitude settings of a transverse vibration grid.
Fig. 6 is a graph of time-averaged flow rate over time at tank station a.
Fig. 7 shows a process diagram of the concentration change of suspended solids at the water tank measuring point A.
FIG. 8 is a flow velocity vector diagram in a grid turbulence field.
Figure 9 is a contour filling map of the longitudinal flow rate U.
The contour profile of the longitudinal flow velocity U of fig. 10.
Fig. 11 transient field of suspended mass sediment concentration (t=30s).
Detailed Description
The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
A method for simulating a turbulence field and a suspended sediment concentration field under grid disturbance comprises the following specific steps:
s1, constructing a fluid control equation by a large vortex simulation (LES) model of double-fluid space filtration based on a level set equation:
wherein phi is a defined level set function; zeta type toy i In the form of a grid of coordinates,is a conversion matrix; j is the Jacobian matrix of the conversion matrix; u (U) i To control the flux of the body; u (u) i Is the flow rate component; ρ is the density; μ is the dynamic viscosity coefficient; p is the pressure, τ li Is the compressive lattice stress (SGS) tensor; kappa is the surface curvature; delta ij Is a Kronecker trigonometric function; h is a smooth Heaviside function; re, fr and We are the dimensionless Reynolds number, froude number and Weber number, respectively, defined as follows:
wherein U and L are respectively a characteristic flow rate and a characteristic lengthA degree; g is gravity acceleration; ρ water Sum mu water The density and viscosity coefficient of water respectively; σ is the surface tension.
S2, establishing a level set model, tracking the fluctuation of the free water surface by using a level set function method, calculating the density and viscosity of the water phase and the air phase by using a level set function phi,
ρ(φ)＝ρ air +(ρ water -ρ air )h(φ)
μ(φ)＝μ air +(μ water -μ air )h(φ)
where φ is a signed distance function, positive in water phase, negative in air phase, constant in density and viscosity, smooth transitions near the crossing interface, and h (φ) is a smooth Heaviside function as defined below as distance 2 ε:
s3, the free water surface is a set with a distance function phi of zero, and a level set equation suggested by the Osher and Sethian is solved to obtain:
solving the quality conservation constant weight initialization equation suggested by Sussman and Fatemi. The poisson pressure equation was solved using an efficient matrix-free Newton-Krylov solver to calculate the level set equation discretely and using the GMRES method of multiple grid pretreatment. The level set equation is spatially discrete using the 3 rd order WENO format and temporally discrete using the 2 nd order range-Kutta format. The reinitialization step uses 2 nd order ENO format calculations.
S4, integrating a fine particle sediment flocculation model based on a sediment particle group equation. Dividing the flocculation group into N discrete groups, using the parting dimension N f Fractal characteristics describing the ith flocculation group:
wherein m is i ，D i ，ρ f,i Respectively representing the mass, diameter and density of the ith flocculation group, D p Is the major particle diameter. Each group of flocculation groups corresponds to a representative size, the group size is the main particle diameter D p To the maximum floc size D max Logarithmic distribution between the flocculation groups according to the size range [ D ] min ，D max ]And (5) automatic adjustment.
The sediment particle exchange among the flocculation groups adopts a double-body interaction mode, is controlled by the aggregation, shearing and crushing and collision crushing of the flocculation groups, and leads to the capturing and losing of the sediment particles, and the general equation is as follows:
wherein n is k The number (m-3) of sediment particles in the kth group of flocculation groups; g aggr And L aggr The sediment particle capturing and losing number (m-3) caused by the flocculation polymerization; g break-shear And L break-shear The sediment particle capturing and losing number (m-3) caused by shearing and crushing respectively; g break-call And L break-call The number (m-3) of sediment particle capturing and losing caused by collision and breaking of the flocculation.
S5, treating boundary conditions by using an immersed boundary method. Taking the grid as a solid and the water body in the water tank as a fluid in an intrusion boundary method; the aperture ratio of the grid meets the condition of generating approximately isotropic turbulence, the local encryption grid can reflect the shape and the distance of local grid holes, and the LES method is applied to simulate the approximately isotropic turbulence field generated by grid oscillation, and the grid moves in a sine function mode in the transverse direction:
L＝A·sin(f·2πt)
where A is amplitude (cm), f is vibration frequency (Hz), t is time(s), and L is grid position (cm).
S6, solving a fluid control equation by adopting a split-step method, wherein a momentum equation adopts a 2-order precision central differential format discrete space-time term comprising viscosity, pressure gradient and SGS term, adopts a 3-order precision WENO format or a 2-order central differential format discrete convection term, and adopts a 2-order precision Crank-Nicholson format to perform time propulsion:
where n represents the previous time step, Δt is the time step, F is the right hand term excluding the pressure term in the 2 nd control equation in step S1, and P is the pressure term.
S6, applying a continuity condition at the 2 nd stage of the splitting step by adopting a 3-point center differential format, and solving the following poisson pressure equation:
where n is a pressure correction term used to update the pressure and velocity fields calculated in step 1 of the splitting step:
p n+1 ＝p n +∏
s7, setting initial conditions and boundary conditions of the mathematical model, wherein the initial conditions are set to turbulent flow velocity and suspended sediment concentration, and the boundary conditions are set to be periodic boundaries. The operation model outputs a turbulent flow field and a suspended mass sediment concentration field under the disturbance of the simulated grid
The following describes embodiments of the present application and simulation results in detail by way of one example with reference to the accompanying drawings.
Case: turbulence field and suspended sediment concentration field simulation under grid disturbance
Case introduction: the test conditions of the physical model test 1 are as follows: the concentration of the mixture is 15kg/m 3 The grating amplitude was 5cm and the vibration frequency was 5Hz. Finally, the average value of the measured concentration is 14.921kg/m 3 . The initial conditions of the numerical simulation turbulence and suspended sediment concentration fields are respectively set to be 0m/s and 15.0kg/m 3 The turbulent flow and the concentration convergence of suspended sediment to a fully developed state can be accelerated. The boundary conditions are set according to the periodic boundaries, as are tests of square tanks and transverse vibrating gratings.
The method for simulating the turbulence field and the suspended sediment concentration field under grid disturbance comprises the following steps:
numerical simulations over at least 1 minute will produce conditions that tend to be random in the course of turbulence and suspended sediment concentration fields.
According to the implementation condition of the physical model test, the position of one observation point A is selected, and the time sequence process of the average value of the flow speed and the average value of the suspended sediment concentration is extracted, as shown in fig. 6 and 7.
Simulations were performed on the flow velocity vector in the tank, the contour fill and the contour distribution of the mean value at longitudinal flow, as in fig. 8, 9 and 10.
The suspended load sediment concentration field distribution was simulated as shown in fig. 11.
As the suspended sediment particles are finer and have strong following property with fluid, and the sediment particles and the fluid turbulence have strong following property, the fine sediment particles can generate flocculation sedimentation, and the interaction between flocculation groups and the fluid turbulence results in aggregation and breaking of the flocculation groups, and finally, a random variation turbulence field of the suspended sediment concentration is formed, as shown in figure 11, the size variation of the suspended sediment concentration is related to the space-time distribution of the turbulence, and the average value of the size-alternate distribution is about 14.9kg/m as shown in figure 11 3 Matching with the measurement average value of the physical model test.
The above embodiments are merely illustrative of the technical solutions of the present application. The method of constructing the hydrological model parameter time-varying form according to the present application is not limited to that described in the above embodiments, but is subject to the scope defined in the claims. Any modifications, additions or equivalent substitutions made by those skilled in the art based on the embodiments of the present application are within the scope of the present application as claimed.
Claims (7)
1. A method for simulating a turbulence field and a suspended sediment concentration field under grid disturbance is characterized by comprising the following specific steps:
s1, establishing a fluid control equation of a large vortex model of double-fluid space filtration based on a level set equation;
s2, establishing a level set model in the model, and tracking the fluctuation of the free water surface by using a level set function method;
s3, classifying and describing flocculation polymerization and splitting processes based on the size of sediment particles in a model;
s4, treating the solid-liquid two phases in the model by using an immersed boundary method;
s5, solving a model control equation by adopting a split step method;
s6, simulating a turbulent flow field and a suspended mass sediment concentration field under the disturbance of the output grid.
2. The method for simulating a turbulent flow field and a suspended sediment concentration field under grid disturbance according to claim 1, wherein the step S1 of establishing a fluid control equation of a large vortex model of double fluid space filtration based on a level set equation comprises the following specific steps:
and constructing a turbulence model control equation by using a large vortex simulation model of double-fluid space filtration based on a level set:
wherein phi is a defined level set function; zeta type toy i In the form of a grid of coordinates,is a conversion matrix; j is the Jacobian matrix of the conversion matrix; u (U) i To control the flux of the body; u (u) i Is the flow rate component; ρ is the density; μ is the dynamic viscosity coefficient; p is the pressure, τ li Is the compressive lattice stress tensor; kappa is the surface curvature; delta ij Is a Kronecker trigonometric function; h is a smooth Heaviside function; re, fr and We are the dimensionless Reynolds number, froude number and Weber number, respectively, defined as follows:
wherein U and L are respectively a characteristic flow rate and a characteristic length; g is gravity acceleration; ρ water Sum mu water The density and viscosity coefficient of water respectively; σ is the surface tension.
3. The method for simulating a turbulent flow field and a suspended sediment concentration field under grid disturbance according to claim 1, wherein the specific steps of the step S2 are as follows:
s21, the level set function phi is a signed distance function, the water phase is positive, the air phase is negative, the density and viscosity in each phase are constant values, the transition is smooth near the crossing interface and varies along with the distance 2 epsilon, the density and viscosity in the water phase and the air phase are calculated by using the level set function phi,
ρ(φ)＝ρ air +(ρ water -ρ air )h(φ)
μ(φ)＝μ air +(μ water -μ air )h(φ)
h (φ) is a smooth Heaviside function defined as follows:
s22, the free water surface is a set with a distance function phi of zero, and a level set equation is solved to obtain:
s23, after solving the level set convection equation, the distance function is not guaranteed to be a unit gradient, the conservation of mass of two phases is guaranteed, and in order to solve the problem of non-conservation, the model solves the mass conservation constant weight initialization equation.
4. The method for simulating a turbulent flow field and a suspended sediment concentration field under grid disturbance according to claim 1, wherein the specific steps of the step S3 are as follows:
s31, dividing the flocculation group into N discrete groups, and using the parting dimension N f Fractal characteristics describing the ith flocculation group:
wherein m is i ，D i ，ρ f,i Respectively representing the mass, diameter and density of the ith flocculation group, D p Is the major particle diameter;
s32, each flocculation group corresponds to a representative size, and the grouping size is the main particle diameter D p To the maximum floc size D max Logarithmic distribution between the flocculation groups according to the size range [ D ] min ，D max ]Automatically adjusting;
s33, sediment particle exchange among flocculation groups adopts a double-body interaction mode, is controlled by aggregation, shearing crushing and collision crushing of flocculation groups, and causes the capture and loss of sediment particles, and the general equation is as follows:
wherein n is k The number (m-3) of sediment particles in the kth group of flocculation groups; g aggr And L aggr The sediment particle capturing and losing number (m-3) caused by the flocculation polymerization; g break-shear And L break-shear The sediment particle capturing and losing number (m-3) caused by shearing and crushing respectively; g break-call And L break-call The number (m-3) of sediment particle capturing and losing caused by collision and breaking of the flocculation.
5. The method for simulating the turbulence field and the suspended sediment concentration field under the disturbance of the grid according to claim 1, wherein the specific implementation step of the step S4 is as follows:
s41, taking the grid as a solid and taking the water body in the water tank as a fluid in an intrusion boundary method; the aperture ratio of the grid meets the condition of generating turbulence similar to isotropy, and the local encryption grid can reflect the shape and the spacing of local grid holes;
s42, simulating an approximately isotropic turbulence field generated by grid oscillation by using an LES method, wherein the grid moves in a sine function mode in the transverse direction:
L＝A·sin(f·2πt)
wherein A is amplitude, f is vibration frequency, t is time, and L is grid position;
s43, various working conditions of a physical model test can be generated by adjusting the vibration frequency and amplitude of the grid so as to realize effective simulation of a turbulence field and a suspended mass sediment concentration field under grid disturbance.
6. The method for simulating the turbulence field and the suspended sediment concentration field under the disturbance of the grid according to claim 1, wherein the specific implementation step of the step S5 is as follows:
s51, solving a fluid control equation by adopting a split-step method, wherein a momentum equation adopts a 2-order precision central differential format discrete space-time term comprising viscosity, pressure gradient and SGS term, adopts a 3-order precision WENO format or a 2-order central differential format discrete convection term, and adopts a 2-order precision Crank-Nicholson format to perform time propulsion:
where n represents the previous time step, Δt is the time step, F is the right hand term excluding the pressure term in the 2 nd control equation in step S1, and P is the pressure term.
S52, applying a continuity condition at the 2 nd stage of the splitting step by adopting a 3-point center differential format, and solving the following poisson pressure equation:
where n is a pressure correction term used to update the pressure and velocity fields calculated in step 1 of the splitting step:
p n+1 ＝p n +Π
7. the method for simulating the turbulence field and the suspended sediment concentration field under the disturbance of the grid according to claim 1, wherein the specific implementation step of the step S6 is as follows:
s61, setting initial conditions and boundary conditions of a mathematical model, wherein the initial conditions are set to turbulent flow velocity and suspended sediment concentration, and the boundary conditions are set to be periodic boundaries.
S62, operating the model, and outputting a turbulent flow field and a suspended solid sediment concentration field under the simulated grid disturbance.
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