IMPACT ON MOVABLE MODEL OF TIME DISTORTION RATIO ANALYSIS[1]

Zhang Junhua², Zhao Lianjun³, Yang Ming³ and Ma Huaibao³

2. Ph.D. Prof. Beijing University of Aeronautics and Astronautics, Beijing 100083,China

3. Engineer, Institute of Hydraulic Research,YRCC,Zhengzhou 450003,China

Abstracts: Based on Xiaolangdi~Sushizhuang prototype and model , to study the impact on movable model of time distortion ratioη_t by using  the unsteady flow mathematical model which is suitable for prototype and model at the same time. Give out the deviation intensity of bedform deformation and model hydraulic factors with differentη_t in quantity. 

Keywords: time distortion ratio, movable model, mathematical model

1    INTRODUCTION

Sediment movable model has time scaleλ_t1 deduced from flow continuity similar and time scaleλ_t2 deduced from bedform deformation similar, the two scales are not equal in general. For the chief purpose of sediment movable model is to study the bedform deformation problems, soλ_t2 be used to control the model release water time and  time distortion ratio problem produced. It will bring serious questions if the time distortion η_t =λ_t2/λ_t1 too large. As the discharge process at entrance and the stage process modification at the export controlling according toλ_t2, however, the model flow transport process abided by the flow continuity similarity scale of λ_t1, it cause discharge and stage process in some cross-sections distortion, and affect the bedform deformation similar sequentially.It is short of research achievement of time distortion ratio η_t impacts on model stage, discharge, bedform deformation in quantity at present.This paper present a way of carrying out the research with the assistance of mathematical model, give out error values caused by time distortion in quantity. The research method can not only improve the precision of sediment movable model simulating but also open up a way of optimizing model design.

2    RESEARCH CONDITION

2.1    Research method

Based on the prototype and model from Xiaolangdi to Sushizhuang in the lower Yellow River, created unsteady flow mathematical model suit for prototype and model at the same time. By using typical year field measured data,aims directly at the different

time distortion ratio η_t and corresponding sediment concentration scaleλ_s ,calculating flood process and volume of erosion and siltation,frequently,analyzing the impact on flood process and bedform deformation of time distortion ratio.

2.2    Physical model condition

It’s about 250 Km in prototype from Xiaolangdi to Sushizhuang in the lower Yellow River, most of the river reach are wavering type.The river bed wide,shallow and straggle,scour and silation intensity are powerful and the main stream sways frequently.According to the size of experiment field and satisfy the distortion ratio,horezontal scale of the model is taken as λ_L =600 and vertical scaleλ_H =60.Coal crumbs with stable characyerisics of physics and chemistry of Zhengzhou power plant are taken as the model sand after comparison.

In model design process, sediment carry capacity formula of Zhanghongwu is adopted and sediment concentration scale is determined by materials of experiment.

                        (1)

in which:κ is Von Karman’s constant;  is specific weight of muddy water,ω is settling velocity of sediment particles in muddy water;V is velocity;h is water depth;D₅₀ is median diameter of bed materials;S_v is sediment concentration in volume; ξ is correlated coefficient of specific weight defined by

                               (2)

For introduced coefficient ofξ,formula(1) could fit well with prototype sand and physical model sand. The chosen coal crumbs of Zhengzhou power plant  is about 2.1t/m³, theξ=2.5; as to prototype sand, _s=2.7 t/m³, the=1.

By using the prototype quantity ,physical measured data and the corresponding model scale,prototype suspension capacity (S_*p)and model suspension capacity(S_mp) can be drawn respectively.Numerous data indicate that the various scope of  S_*p/S_mp is from 1.67 to 2.25.Time scale deduced  from the river bedform  deformation equation.For river bed deformation similarity criterion combines the time scale of _t2 with sediment concentration of _s,the corresponding time scale of river bed deformation can be calculated out        _t2=66.5~89.5,the time scale of model   flow movement _t1=77.5.

For the suspension capacity formula  is a semi-emperical theory ,and limits to the precision of measured data,sediment concentration scale of initial design may change in  some way. In general ,model test definite the sediment concentration scale and time scale at last.By model testing, modify the scale,the model can replay the  prototype porcess and ensure the flow condition ,sediment movement and bedform deformation measured in the model similar with prototype situation.By experiment test of 1982 typical flood,the sediment movable model of Xiaolangdi~Sushizhuang  define the sediment concentration scale _s =1.8 and time scale _t=83.

2.3    Mathmatical model condition

The chosing water and sediment movement foundation equations are as follows.

Water continuity equation

                       (3)

Water movement equation

                     (4)

Sediment continuity equation

   (5)

River bed deformation equation

                      (6)

In which, Q is discharge; A is wetted cross-sectional area; t is time; x is fluid coordinate;Z is water stage;K is discharge modulus;α₁ is coefficient of momentum correction;S is sediment concentration;R is specific weight of deposit sand;b_ij is width of sub cross-section ;Z_bij is the elevation of  sub cross-section; m is the sub cross-section numbers;f₁ is the unsaturation coefficient ;k₁ is the correction coefficient; a_* is the coefficient of balance sediment discribution.

In addition, introducing the Zhanghongwu suspension capacity formula, Zhaolianjun river bed roughness formula,formula of suspension grain percentage and bed load grain percentage calculating and exchanges,suspension concentration  distrbution in crosswise etc.It should be say,all above formulas fit well with both prototype sand and model sand.

Adopt the measured terrain and flood process data of 1977 and 1982 year from Xiaolangdi to Gaocun in the lower Yellow River to test the mathematical model,the calculating result of flood sediment transport process,water stage variety,bedform deformation and sediment grain percentage modification be in line with the prototype data.

Calculating by using movable sediment model boundary terrain,model sand characteristics index and transfigured flood process abided by corresponding scale of _q, _s and _t as boundary condition and flood sediment condition,with the correlated scale to return the calculating result to prototype,the flow movement, sediment transport and bedform deformation are agree well with prototype.

In a word,the unsteady flow sediment mathematical model has the  function of simulating the prototype and movable sediment model at the same time,and be an efficient instrument to carry out the research work.

3    IMPACT ON TIME DISTROTION ANALYSIS          

By the created unsteady mathematical model,chosing a flood process of August,1982 as water sediment condition,take the before-flood terrain of 1982 as original terrain,the calculating result of flood process,flood stage process and volume of erosion or siltation  as the comparison foundation.

As above mentioned,on the design process of Xiaolangdi~Sushizhuang model, the sediment concentration scale be in a extent,and the correlated time scale is not a fixed quantity but define it by model testing.In fact,the model have the time distortion ratio too,time scale distortion ratio η_t=1.07;It can calculate out the impact on time scale distortion by created unsteady flow mathematical model;As for comparison condition, time distortion ratioη_t =1,just the model has no distortion;As for sensitive analysis,take the sediment concentration scale as 1.0 and 3.0 differently,the corresponding time scale are 150 and 50,time distortion ratio are 1.93 and 0.64 to calculating and analyzing.

Taking the before-flood terrain of 1982 to contract with geometry scale as boundary condition, according to the discharge scaleλ_L and concentration scaleλ_s to transfer the measured inflow and sediment into  model water sediment process,then calculating  out the flood process and volume of erosion and siltation of different η_t conditions, compare with calculating result based on prototype material after returning to prototype.

3.1    Impact on flow movement of time distoriton ratio

Fig. 2    Calculating result of discharge process in different time   distortion ratio on Jiahetan cross-section

Fig. 3    Calculating result of discharge process in different time distortion ratio on Gaocun cross-section

3.2    Impact on bedform deformation of time distortion

For model flow movement not similar with prototype,the model hydraulic factors have some deviations with prototype, and the sediment movement is not similar either,sequentially,affect the bedform deformation similarity.Table 1 give out calculating result of erosion and siltation volume in different η_t of prototype model respectively.When η_t =1.07,model is alike prototype; η_t =1.,there are some deviations between prototype with model,and that is why take λ_s =1.8, λ_t =83 but not λ_s =1.93 ,λ_t =77.5 in Xiaolangdi ~ Sushizhuang model after model testing.

Table 1    calculating result of  erosion and siltation volume from Xiaolandi to Gaocun

To make a comprehensive analysis of calculating result above,given that λ_s =1.8,       λ_t2 =83,the time distortion is suitable, it can satisfy the flow movement and bedform deformation similarity; and agree well with the conclusion of model test at the same time.

Something should be mentioned that,in order to reduce all kinds of deviations caused by time distortion ratio in the formerly research,two steps put into practice to save the situation. First, to set the next discharge grade ahead of the schedule in the entrance,enlarge the discharge while flood fall in some degree,to accoplish the channel impounding process in a short time by control;Second,modify the export stage according to the design requirement ,in other words,to accomplish the process of back water go upstream by intentionaly stage change ratio.By our research,the conclusion in file[5] that” the way of adjusting intake or export stage have finite advantage, if the two time scales differ greatly in some long-distance river models,not only the effective amending actions do not work,but also the actions have new deviations.” is correct.

4    CONCLUSION

(1) There have extremely important meaning to study the scales of  river  model in quantity by unsteady mathematical model,but the chief condition is that the mathematical model could simulate  the model and prototype accurately at the same time.

(2) If λ_t2>λ_t1,then the discharge peak reduced in the flood transport process,flood peak sluggish and discharge courses figure become short and fat,whileλ_t2<λ_t1, discharge peak enlarge and in advance,discharge courses become thin.The deviation become larger with the  η_t greaten and with the river reach longer the deviation more marked.

(3) Because of the time distortion ratio,the deviations of model hydraulic factors cause the  bedform deformation not similar with prototype, the error become larger with the  increasing deviation of λ_t2 and λ_t1.

(4) The research method can employ in sediment movable model design and have important practical value in optimizing model scale.

References

[1]    Xie jianheng(ed.).River Simulation. Water Resource and Electronic Power Press. Beijing(in Chinese),1988.

[2]    Zhanghongwu and Liuhailing. Study of Physical Model Test from Xiaolangdi to Susizhaung in the Lower Yellow River. Institue of Hydraulic Research, YRCC. Zhengzhou, China.(in Chinese).1999.

[3]    Zhanghongwu and Jiangenhui. Simulatary Laws of Hyperconcentration model in Yellow River. Hennan Science and Technology Press. Zhengzhou (in Chinese).1994.

[4]    Zhaolianjun and Zhanghongwu .Mathematical Model Study of Flood Proceeding  from Tiexie to Sunkou in the Lower Yellow River. Institute of Hydraulic Research, YRCC. Zhengzhou, China.(in Chinese).1998.

[5]    Libaoru,Design Method of Movable Model and Some Special Problems in China.Symposium of Institue of Hydraulic Research, YRCC(3^rd.)Chinese Environment Science Press ,1992(1-16).