CN111351609A - Method for measuring wall shear stress vector - Google Patents

Abstract

The invention provides a method for measuring wall shear stress vector, which belongs to the technical field of fluid mechanics experiment. The measurement structure used in the method for measuring the wall shear stress vector of the present invention is composed of two calibration-free hot film sensors installed on the wall surface perpendicular to each other. The two sensors are identical in size and construction. The principle of free calibration of the sensor is realized by using double-layer nickel foil to block the heat transfer from the thermal film as the sensitive element to the wall. Collect the voltage and current of the two sensors and calculate the heating power of the two sensors. Combined with the positional relationship between the two sensors, the magnitude and direction of the wall shear stress can be calculated. This method can measure the magnitude and direction of wall shear stress without calibration.

Description

A Measurement Method of Wall Shear Stress Vector

technical field

The invention belongs to the technical field of fluid mechanics experiments, and relates to a vector measurement method of wall shear stress, which is used to measure the magnitude and direction of wall shear stress in a flow field.

Background technique

The wall shear stress is an important parameter of the wall in the flow field. It can determine the distribution of the viscous force on the wall and the velocity near the wall. The methods of measuring the wall shear stress include direct measurement on the wall and indirect measurement of physical quantities related to the wall shear stress. method. Among them, the microelectromechanical sensor using the principle of heat exchange has been widely used in the field of measurement. In the heat exchange principle sensor, a non-calibrated wall shear stress sensor can measure the magnitude of the wall shear stress, but the sensor cannot identify the direction of the wall shear stress.

SUMMARY OF THE INVENTION

The invention provides a method for measuring the wall shear stress vector, which can measure the magnitude and direction of the wall shear stress in the flow field.

Technical scheme of the present invention:

A method for measuring the shear stress vector of a wall surface: the measuring method consists of two measuring structures consisting of two perpendicular calibration-free hot film sensors installed on the wall surface with the same size and structure. The wall shear stress to be measured between the two sensors in the direction range acts on this measurement structure. At this time, the voltage and current of each calibration-free hot film sensor composing this measurement structure are related to two factors: one is the wall shear stress. The size of the stress, the second is the angle between the direction of the wall shear stress and the installation direction of the calibration-free thermal film sensor. Combining the voltage and current of the two calibration-free hot film sensors, the heating power of the two sensors is obtained, and the magnitude and direction of the wall shear stress can be calculated.

Beneficial effects of the present invention: The present invention constructs a measurement structure composed of two calibration-free thermal film sensors installed on the wall surface perpendicular to each other, and combines the heating power of the two sensors to calculate the wall surface cut at the position of the measurement structure. The magnitude and direction of the stress can be measured only by measuring the voltage and current of the sensor in the measuring structure. It is not necessary to calibrate the measuring structure in use. It is suitable for measuring the magnitude and direction of the wall shear stress but it is not convenient to carry out the case of calibration.

Description of drawings

Figure 1 is a schematic diagram of the structure of a calibration-free hot film sensor.

Figure 2 is the installation position diagram of two calibration-free hot film sensors.

Detailed ways

The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

The schematic diagram of the calibration-free thermal film shear stress sensor based on the principle of heat exchange is shown in Figure 1. The sensor consists of two nickel foils and a layer of polyimide film. The two nickel foils are energized and heated to the same temperature. One of the nickel foils is in direct contact with the fluid in the flow field and exchanges heat with the fluid as a sensitive element. Another piece of nickel foil is installed at the corresponding position on the other side of the polyimide film, as the substrate of the sensitive element, and makes the two pieces of nickel foil work at the same temperature. In this way, the heat conducted by the sensitive element to the wall can be reduced to almost zero. At this time, the heating power Q of the thermal film has the following relationship with the wall shear stress:

Which is derived from the heat transfer theory:

where Tf is the temperature of the nickel foil, Ta is the temperature of the fluid, w is the width of the nickel foil, l is the length of the nickel foil, and k, ρ, Cp, and μ are the thermal conductivity, density, specific heat capacity and viscosity of the fluid, respectively;

According to the formula for the temperature coefficient of resistance, the temperature Tf of the nickel foil is calculated using the following formula:

Among them, T _f is the temperature of the nickel foil, T ₀ is the temperature of the nickel foil at room temperature, α is the temperature coefficient of resistance of nickel, R ₀ is the resistance of the nickel foil at room temperature, and R is the resistance of the nickel foil in the working state. By controlling the current and measuring the resistance, the two pieces of nickel foil can be heated to the same temperature, and the heat transfer between the thermal film and the wall as a sensitive element can be ignored.

The above analysis is based on the conclusion that the angle between the incoming flow direction and the normal direction of the sensor is zero. When the angle between the incoming flow direction and the normal direction of the sensor is α, according to the heat transfer theory, it can be concluded that:

It can be seen that when there is an angle between the incoming flow direction and the normal direction of the sensor, the heating power of the thermal film is compared with the case where the angle is zero, and the heating power is multiplied by the third power of the cosine value of the angle at this time. power.

The measurement structure proposed by the present invention is composed of two calibration-free thermal film sensors mounted on the wall surface. The two thermal film sensors are installed symmetrically and perpendicular to each other, as shown in FIG. 2 . Among them, the angle between the normal direction and the incoming flow direction of the two hot film sensors is α ₁ and α ₂ respectively, the angle between the wall shear stress and the symmetry axis of the two sensors is β, and the working temperature of the two sensors is the same, both T _f , then according to formula (4), the heating powers Q ₁ and Q ₂ of the two thermal film sensors can be expressed in the following form

_In practical applications, Q1 and _Q2 are the voltages and currents through the hot film that can be directly measured and calculated. The unknowns in equations (5) and (6) are the shear stress and the included angle. From the geometric relationship in the schematic diagram,

α ₁ =β-45° (7)

α ₂ =β+45° (8)

Substitute this angle relationship into the

That is, by measuring the heating power of the two sensors, the magnitude and direction of the wall shear stress can be obtained.

Claims (1)

1. a method for measuring wall shear stress vector, characterized in that the measuring method uses two mutually perpendicular hot film sensors installed on the wall surface to measure; the size and structure of the two hot film sensors are exactly the same; the hot film The sensor measures the shear stress of the wall according to the relationship between the heating power and the shear stress of the wall; the hot film sensor is realized by double-layer nickel foil working at the same temperature to block the heat transfer between the nickel foil as a sensitive element and the wall, In order to realize the calibration-free measurement of the sensor; through the conversion of the heating power of the two hot film sensors, the magnitude and direction of the wall shear stress are obtained; the heating power of the two hot film sensors are Q ₁ and Q ₂ respectively, and the wall shear stress The direction β and size τ _w are respectively:

In the formula: Q ₁ and Q ₂ represent the heating power of the hot film sensor; A is a constant derived from the heat transfer theory according to the sensor size and the working temperature difference.

Images