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PUBLISHED DATE: - 08-12-2024
DOI: -
https://doi.org/10.37547/tajet/Volume06Issue12-05
PAGE NO.: - 44-50
CALCULATION OF A HYDRODYNAMIC
MODEL FOR CONTROLLING THE MOISTURE
TRANSFER REGIME
Ernazarov Azizbek Ilkhomjon Ugli
Scientific Research Institute Of Irrigation And Water Problem, Tashkent,
Uzbekistan
Sadiev Umidjon Abdusamadovich
Scientific Research Institute Of Irrigation And Water Problem, Tashkent,
Uzbekistan
Jovliev Uktam Temirovich
Scientific Research Institute Of Irrigation And Water Problem, Tashkent,
Uzbekistan
INTRODUCTION
Due to the fact that soil pores are mostly small in
size, the effect of water entering the pores differs
in a number of features. In this regard, the only
thing that can be established by simple
observation is that the larger the pore size, the
coarser the mechanical composition, i.e. these are
large particles that make up the soil. [5,6]. During
the simulation, it was assumed that the particles
are evenly spaced with respect to each other. In
other words, we presented the soil porosity in the
form of a spatial three-dimensional grid
consisting, as it were, of nodules (pores) of
various shapes and sizes connected to each other
by constrictions (narrower passages between the
RESEARCH ARTICLE
Open Access
Abstract
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pores).
The purpose of the research was to create
a hydraulic model describing the relationship of
the moisture transfer regime using the full-scale
parameters of the object of study, the dynamics of
moisture changes in hydromorphic media for an
arbitrary moment of time caused by changes in
the groundwater level and the establishment of its
adequacy were considered [7,8]. Since the
problem of establishing the relationship between
surface and groundwater in the tasks of land
reclamation and engineering hydrology arises
quite often, conducting field research to establish
this relationship is a time-consuming and
expensive undertaking. Therefore, an urgent task
is to develop a hydraulic model that adequately
describes this relationship. Numerical verification
of the simulation results was carried out on the
basis of data obtained during field research in the
farm
“Karshiev
Temurbek”
located
in
Kashkadarya region
MATERIALS AND METHODS
In the numerical implementation of the hydraulic
model of moisture transfer (1), developed during
scientific research, the full-scale parameters of
the object of study were used. That is, field studies
have established that the area of the experimental
site is 6 hectares, the mechanical composition of
the soil is light and medium loam, the fractional
composition is from 0.001 to 0.25 mm. It was also
found that within the study area, the depth of
groundwater is on average one and a half meters.
Capillary rise height
𝐻 = 149 𝑠𝑚
. Using the
formula for determining the capillary rise height
for unsaturated rocks
𝐻 = −𝜓 + 𝑧
; by
𝑧 =
150 𝑠𝑚
, we find the suction height
𝜓 = 1
. The
suction height at full saturation is zero. With
decreasing humidity, the suction height increases
in absolute value.
𝜃 (𝑧
∧
, 𝜏) =
𝑒
−𝛾𝜏
𝛥
0
{
[𝑒𝑥𝑝(
𝑃𝑒(1−√𝐷)
2
𝜓
∧
) − 𝑒𝑥𝑝( 𝜆𝜓)
∧
] 𝑒𝑥𝑝(
𝑃𝑒(1+√𝐷)
2
𝑧
∧
) + + [𝑒𝑥𝑝( 𝜆𝜓)
∧
− 𝑒𝑥𝑝(
𝑃𝑒(1−√𝐷)
2
𝜓
∧
)] 𝑒𝑥𝑝(
𝑃𝑒(1−√𝐷)
2
𝑧
∧
) }
(1)
where:
𝐷 = 𝑃𝑒
2
− 4𝛾𝑃𝑟
, here,
𝑃𝑟 =
𝑃𝑒
𝑅𝑒
- the Prandtl diffusion number,
𝑅𝑒 =
𝑢
фил
𝑙
𝜅
0
Reynolds number and
𝑃𝑒 =
𝑢
фил
𝑙
𝜅
- the Peclet number, empirical coefficients:
𝛾 = 3,5
and
𝜆 = 1
Dependence of the suction height on humidity
𝜓(𝜃)
is different in different breeds and is
determined experimentally. For our calculations, this dependence is presented in the form of the
following relations:
𝜓 = 2𝐻
𝑘
(1 − 𝜃) + 𝐻
0
𝜃 =
𝜃−𝜃
0
𝜃
𝑚
−𝜃
0
(2)
Where:
- soil moisture;
𝜃
𝑚
- full moisture capacity;
𝜃
0
- humidity corresponding to the maximum
molecular;
𝐻
𝑘
- the reduced height of the capillary rise;
𝐻
0
- pressure surge at full saturation.
RESEARCH RESULTS
It should be noted that the relationship between
suction height and humidity is ambiguous. Thus,
when draining a pre-fully saturated rock, the
relationship between humidity and suction height
is characterized by a curve, where each value
𝜓
corresponds to the maximum possible humidity
value.
In the reverse process, when dry soil is moistened,
minimum humidity values are characteristic for
the same suction heights. These two curves form
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two main branches of hysteresis. We all know that
the sorption of water vapor by soil, like many
other adsorbents, is accompanied by the
phenomenon of so-called hysteresis. This
phenomenon consists in the fact that if we
saturate the same canopy of any soil with
moisture at the beginning, placing it sequentially
in a series of spaces with increasing relative
humidity and bringing it to full equilibrium in
each space, and then we will dehydrate the same
canopy by placing it in the same space, but in the
reverse order, i.e. with decreasing relative
humidity, then in the second case (i.e. during
dehydration), the amount of sorbed moisture at
the same relative humidity will always be higher
than in the first (i.e., during watering). The change
of drying and humidification processes forms an
infinite set of hysteresis sweep curves in the area
bounded by the main branches of dependence
𝜓(𝜃)
.
The moisture transfer coefficient is also
significantly dependent on humidity. This
dependence relates the moisture transfer
coefficient and humidity to a power function:
𝜅 = 𝜅
0
𝜃
𝑛
(3)
Where:
𝜅
0
- filtration coefficient.
For homogeneous soil,
n
varies from 1 to 4.
However, in heterogeneous soil, the degree index
can be significantly higher.
To determine the value of the filtration
coefficient, there are various methods:
a) the method of field research;
b) the method of laboratory research;
c) the method of using empirical formulas.
Fig. 1 - Schematic view of field research
The field research method was used to find the
value of the filtration coefficient. To do this, we
drilled 3 shafts in the form of a single cube (with a
volume of 1 m
3
) to the studied soil at an
experimental site with a distance of 0.30 meters
(Fig.1).
The slope of the bottom of the observation shafts
was lowered by 10 sm. by leveling. Then a 40 cm
layer of water was poured into the working pit
and a constant level was maintained by supplying
water (in a volume of 0.2 liters). The research was
carried out until water (a wet spot) appeared on
the walls of the observation pits. That is, 39 hours
later, a wet spot appeared on the walls of the
observation shafts. Using a well-known formula to
determine the filtration rate:
𝑢
𝑓𝑖𝑙𝑡𝑟𝑎𝑡𝑖𝑜𝑛
=
𝑠
𝑡
= 𝜅
0
𝐻
𝑙
(4)
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where:
𝑡 = 39 ℎ𝑜𝑢𝑟𝑠
- time of appearance
of water (humidity) on the wall of the observation
shaft;
𝐻 = 39,5 𝑠𝑚
- the difference between the
marks of the water surface in the working pit and
the wet spot in the observation shaft;
𝑙 = 30 𝑠𝑚
- the distance between the walls
of the working and observation shafts;
𝑠 = √𝑙
2
+ ℎ
2
≈ 30 𝑠𝑚
- the shortest path
traveled by water from the working shaft to the
observation shatf;
ℎ = 0,5 𝑠𝑚
- the difference between the
marks of the bottom of the working shaft and the
wet spot.
DISCUSSION
Considering the full-scale data and formulas (3)
and (4), for medium loamy soils, the following
values were obtained:
𝑢
𝑓𝑖𝑙𝑡𝑟𝑎𝑡𝑖𝑜𝑛
= 0,77
𝑠𝑚
ℎ𝑜𝑢𝑟
,
𝜅
0
= 0,585
𝑠𝑚
ℎ𝑜𝑢𝑟
=
0,14
𝑚
𝑑𝑎𝑦
,
𝜃 = 20,44
,
𝜅 = 11,96
𝑠𝑚
ℎ𝑜𝑢𝑟
(5)
Before proceeding to the numerical
implementation of equation (1), it is necessary to
determine
the
numerical
values
of
geohydrodynamic similarities. In this regard,
using the parameters of field studies and (5), we
obtain:
𝑃𝑟 = 0,49
,
𝑅𝑒 = 39,5
and
𝑃𝑒 = 19,31
. (6)
Given the equations (1), (5), (6) after the
appropriate mathematical transformations, we
obtain the solution of equation (1). They are
presented in the form of graphs (Fig.2-9).
Fig 2. - Graph of the function
𝜽(𝝉, 𝒛)
at a depth of up to 20 cm.
Fig 3. - Graph of the function
𝜽(𝝉, 𝒛)
at a depth of up to 40 cm.
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Fig 4. - Graph of the function
𝜽(𝝉, 𝒛)
at a depth of up to 80 cm.
Fig 5. - Graph of the function
𝜽(𝝉, 𝒛)
at a depth of up to 120 cm.
Fig 6. - Graph of the function
𝜽(𝝉, 𝒛)
for 5 hours.
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Fig 7. - Graph of the function
𝜽(𝝉, 𝒛)
for 24 hours.
‘
Fig 8. - Graph of the function
𝜽(𝝉, 𝒛)
for 50 hours.
Fig 9. - Graph of the function
𝜽(𝝉, 𝒛)
CONCLUSION
A numerical experiment of a hydraulic model for
controlling the moisture transfer regime using the
full-scale parameters of the object of study is
performed, the dynamics of moisture changes in
hydromorphic media for an arbitrary moment of
time due to changes in the groundwater level is
considered
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The obtained patterns of changes in soil moisture
allowed us to establish the nature of changes in
moisture transfer at various depths of the soil
cover.
ACKNOWLEDGEMENTS
This publication has been produced within the
framework of the Grant «Development of
hydraulic technologies for managing of soil
moisture during furrow irrigation of agricultural
crops» (REP-24112021/66), funded under the
MUNIS Project, supported by the World Bank and
the Government of the Republic of Uzbekistan.
The statements do not necessarily reflect the
official position of the World Bank and the
Government of the Republic of Uzbekistan.
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