DE102017203254A1 - Method for determining a leakage area of a fuel tank - Google Patents

Abstract

The present invention relates to a method for determining a leakage area A _{leak of} a fuel tank with the steps i) pressure build-up under pressure generation in the fuel tank, ii) measurement of a pressure drop over a measuring time (t) and iii) determination of the leakage area A _leak .

Description

State of the art

The present invention relates to a method for determining a leakage area of a fuel tank, wherein the leakage area is, in particular, outgassing of fuel constituents via the fuel tank.

From the prior art methods for detecting a leakage of a fuel tank are known. For example, describes DE 102013012881 A1 a method for detecting a leak in a fuel system of a motor vehicle with a fuel tank, a fuel pump and a pressure sensor for detecting an internal pressure of the fuel tank. In a first step, a pumping power of the fuel pump is set in such a way in dependence on at least one precondition that a pumping movement of the fuel takes place within the fuel system. In a second step, an increase in pressure within the fuel tank is detected by means of the pressure sensor and in a third step, a value of the pressure increase is compared with a predetermined threshold value. In a fourth step, a leak is detected when the value of the pressure increase is less than the threshold value. A disadvantage of the known method is that only can be determined whether a leak in the fuel tank is present or not. A leakage area is therefore not determinable.

Disclosure of the invention

The inventive method according to claim 1 overcomes this disadvantage. According to the invention, a method is thus specified with which a leakage area can be determined. For the purposes of the present invention, a leakage surface is understood to mean, in particular, an area of outgassing of fuel constituents from a fuel tank. In accordance with legal requirements, certain limit values must be observed for environmental reasons and for reasons of health protection for gas emissions from tank systems. The method according to the present invention can help to make fuel tanks safer and also denser in order to meet the legal requirements, because for this the knowledge of a leakage area is essential.

In a first step, a pressure is built up in the fuel tank under pressure generation. Subsequently, a pressure drop is determined over a predetermined measuring time and from this the leakage area is determined. In other words, the measurement time required for evacuation of fuel components from the fuel tank between a predetermined first pressure and a predetermined second pressure is determined. The determined measuring time is directly proportional to the leakage area. The method is simple, without high technical complexity and thus cost feasible and allows a precise determination of a leakage area of a fuel tank.

The dependent claims show preferred developments of the invention.

According to an advantageous development of the pressure build-up is carried out by means of a volume flow pump. Volumetric pumps are commonly used in fuel supply systems and are also used for rinsing activated carbon beds in fuel tanks. The procedure given here is therefore particularly cost-effective.

Further advantageously, the leakage area is determined by solving the following equation (1): $${\text{A}}_{\text{leak}}=\left[\left({\text{p}}_1-{\text{p}}_{\text{2}}\right)*{\text{V}}_{\text{T1}}\right]/\left[{\text{v}}_2*{\text{R}}_{\text{s}}*\text{T}*\text{t}*{\mathrm{\rho }}_{\text{T}}\right]$$

In equation (1), A _leak quantifies the _{leak area} to be determined, p ₁ a first pressure in N / m ² , p ₂ a second pressure in N / m ² with p ₂ <p ₁ , ρ _T the air density in the fuel tank in kg / m ³ , R _{s is} the specific gas constant (287 (N * m) / (kg * K)), t is the measurement time in seconds when measuring the pressure drop (p ₁ -p ₂ ), T is the temperature in the fuel tank in Kelvin, V _T1 the air volume in the fuel tank in m ³ and v ₂ the air flow speed in m / s.

In this case, equation (2) also applies: $${\text{v}}_2=\surd \left[2*\left({\text{p}}_{\text{t}}-{\text{p}}_{\text{a}}\right)/{\mathrm{\rho }}_{\text{a}}\right]$$

In equation (2), p _{t is} an average of the pressure in N / m ² between p ₁ and p ₂ , p _{a is} the atmospheric pressure (about 998 hPa with Pa = N / m ² ), where p _t and p _{a are} determined via pressure sensors and ρ _{a is} the air density in the vicinity of the fuel tank in kg / m ³ .

wobei V_T das Volumen des Kraftstoffbehälters in m³ und V_F der Füllstand des Kraftstoffbehälters mit Kraftstoff in m³ ist, und wobei V_F aus einer Tankfüllstandanzeige ermittelt wird.The volume of air in the fuel tank used in equation (1), V _T1 , is available from equation (3) below: $${\text{V}}_{\text{T1}}={\text{V}}_{\text{T}}-{\text{V}}_{\text{F}}$$

where V _{T is} the volume of the fuel tank in m ³ and V _{F is} the fuel level of the fuel tank in m ³ , and V _{F is determined} from a tank level gauge.

The above equation (1) can be derived as follows:

It is assumed that gas (air + outgassing) flows out of a fuel tank. In the vicinity of the fuel tank, the pressure is equal to the air pressure p _a .

wobei p_k der Druck im Kraftstoffbehälter in N/m², ρ_T die Luftdichte im Kraftstoffbehälter in kg/m³, v_t die Strömungsgeschwindigkeit im Kraftstoffbehälter in m/s, p_a der Luftdruck in der Umgebung des Kraftstoffbehälters, ρ_a die Luftdichte in der Umgebung des Kraftstoffbehälters in kg/m³ und v₂ die Luftströmungsgeschwindigkeit in m/s ist.According to the Bernoulli equation (6): $${\text{p}}_{\text{k}}=1/2*{\mathrm{\rho }}_{\text{T}}*{\text{v}}_{\text{t}}{}^2={\text{p}}_{\text{a}}+1/2*{\mathrm{\rho }}_{\text{a}}*{\text{v}}_2{}^2$$

where p _{k is} the pressure in the fuel tank in N / m ² , ρ _{T is} the air density in the fuel tank in kg / m ³ , v _{t is} the flow velocity in the fuel tank in m / s, p _{a is} the air pressure in the vicinity of the fuel tank, ρ _{a is} the air density in the vicinity of the fuel tank in kg / m ³ and v _{2 is} the air flow velocity in m / s.

Assuming that v _t = 0, after changing from equation (6) v ₂ can be obtained as follows: $${\text{v}}_2=\surd \left[2*\left({\text{p}}_{\text{k}}-{\text{p}}_{\text{a}}\right)/{\mathrm{\rho }}_{\text{a}}\right]$$

From this it can be seen that v _{2 is} a constant, since p _{k has the} same value for all measurements, which corresponds to the mean value p _t between p ₁ and p ₂ . In other words, it may be assumed that the flow rate between two pressures (p ₁ and p ₂ ) for pressures> 20 hPa can be considered proportional.

Furthermore, the following equation (8) applies to the volume flow v̇ ₂ in m ³ / s through the leakage area A _Leak : $${\stackrel{,}{\text{v}}}_2={\text{v}}_2*{\text{A}}_{\text{leak}}=\text{flow rate}*\text{leakage area}$$

wobei m_t1 die Luftmasse im Kraftstoffbehälter beim Druck p₁ und m_t2 die Luftmasse im Kraftstoffbehälter beim Druck p₂ ist. Umgestellt nach der Messzeit t ergibt sich Gleichung (10): $$\text{t}=\left({\text{m}}_{\text{t2}}/{\mathrm{\rho }}_2-{\text{m}}_{\text{t1}}/{\mathrm{\rho }}_{\text{1}}\right)/{\text{v}}_2*{\text{A}}_{\text{Leck}}$$

wobei ρ_i und ρ₂ Luftdichten bei den entsprechenden Drücken p₁ und p₂ im Kraftstoffbehälter sind und für kleine Differenzen (p₂-p₁) als gleich betrachtet werden können: ρ₁=ρ2 = ρ_T.As a consequence of the air mass change per time equation (9) results $$\text{Mass flow:}\left({\text{m}}_{\text{t2}}-{\text{m}}_{\text{t1}}\right)/\text{t =}{\mathrm{\rho }}_{\text{T}}*{\stackrel{,}{\text{v}}}_2={\mathrm{\rho }}_{\text{T}}{\text{* v}}_2*{\text{A}}_{\text{leak}}$$

where m _{t1 is} the air mass in the fuel tank at pressure p ₁ and m _{t2 is} the air mass in the fuel tank at pressure p ₂ . Switched after the measuring time t, equation (10) results: $$\text{t}=\left({\text{m}}_{\text{t2}}/{\mathrm{\rho }}_2-{\text{m}}_{\text{t1}}/{\mathrm{\rho }}_{\text{1}}\right)/{\text{v}}_2*{\text{A}}_{\text{leak}}$$

where ρ _i and ρ _{2 are} air densities at the corresponding pressures p ₁ and p ₂ in the fuel tank and can be considered as equal for small differences (p ₂ -p ₁ ): ρ ₁ = ρ 2 = ρ _T.

Equation (10) shows that the measurement time is inversely proportional to the leakage area.

Switched to the air mass change results equation (11): $$\left({\text{m}}_{\text{t2}}-{\text{m}}_{\text{t1}}\right)={\text{v}}_2*{\text{A}}_{\text{leak}}*\text{t *}{\mathrm{\rho }}_{\text{T}}$$

Furthermore, from the Ideal Gas Law (12): $$\text{p}*{\text{V = m * R}}_{\text{s}}\text{* T}\Rightarrow \text{p}=\text{m}*\left({\text{R}}_{\text{s}}*\text{T}\right)/\text{V}$$

wobei wiederum m_t1 die Luftmasse im Kraftstoffbehälter beim Druck p₁ und m_t2 die Luftmasse im Kraftstoffbehälter beim Druck p₂ ist. Damit ist die Luftmassenänderung (m_t2-m_t1) für die gleiche Druckdifferenz (p₁-p₂) direkt proportional zu den Volumina: $$\left({\text{mt}}_2-{\text{mt}}_1\right)=\left[\left({\text{p}}_{\text{1}}-{\text{p}}_2\right)*{\text{V}}_{\text{T1}}\right]/\left({\text{R}}_{\text{s}}*\text{T}\right)$$

wobei V_T1 das Luftvolumen im Kraftstoffbehälter in m³ ist und über das Volumen des Kraftstoffbehälters V_T in m³ und das Volumen des Kraftstoffs im Kraftstoffbehälter V_F in m³ gemäß Gleichung (3) ermittelbar ist: $${\text{V}}_{\text{T1}}={\text{V}}_{\text{T}}-{\text{V}}_{\text{F}}$$

For the same volume V, between two pressures p ₁ and p ₂ applies: $${\text{p}}_1-{\text{p}}_2={\text{m}}_{\text{t1}}*\left({\text{R}}_{\text{s}}*\text{T}\right)/{\text{V}}_{\text{T1}}-{\text{m}}_{\text{t2}}*\left({\text{R}}_{\text{s}}*\text{T}\right)/{\text{V}}_{\text{T1}}$$

again m _{t1 is} the air mass in the fuel tank at pressure p ₁ and m _t2 the air mass in the fuel tank at pressure p ₂ . Thus, the air mass change (m _t2 -m _t1 ) for the same pressure difference (p ₁ -p ₂ ) is directly proportional to the volumes: $$\left({\text{mt}}_2-{\text{mt}}_1\right)=\left[\left({\text{p}}_{\text{1}}-{\text{p}}_2\right)*{\text{V}}_{\text{T1}}\right]/\left({\text{R}}_{\text{s}}*\text{T}\right)$$

where V _{T1 is} the volume of air in the fuel tank in m ³ and can be determined via the volume of the fuel tank V _T in m ³ and the volume of the fuel in the fuel tank V _F in m ³ according to equation (3): $${\text{V}}_{\text{T1}}={\text{V}}_{\text{T}}-{\text{V}}_{\text{F}}$$

kann nach der Leckagefläche A_Leck umgestellt werden und man erhält Gleichung (1): $${\text{A}}_{\text{Leck}}=\left[\left({\text{p}}_1-{\text{p}}_2\right)*{\text{V}}_{\text{T1}}\right]/\left[{\text{v}}_2*{\text{R}}_{\text{s}}*\text{T}*\text{t}*{\mathrm{\rho }}_{\text{T}}\right]$$

Substituting Equations (11) and (14) as follows $${\text{v}}_2*{\text{A}}_{\text{leak}}*\text{t *}{\mathrm{\rho }}_{\text{T}}=\left({\text{p}}_1-{\text{p}}_2\right)*{\text{V}}_{\text{T1}}/\left({\text{R}}_{\text{s}}*\text{T}\right)$$

can be switched to the leakage area A _leak and gives equation (1): $${\text{A}}_{\text{leak}}=\left[\left({\text{p}}_1-{\text{p}}_2\right)*{\text{V}}_{\text{T1}}\right]/\left[{\text{v}}_2*{\text{R}}_{\text{s}}*\text{T}*\text{t}*{\mathrm{\rho }}_{\text{T}}\right]$$

Thus, it will be appreciated that the time required for the evacuation of a gas from a fuel tank between two predetermined pressures is proportional to the volume of air in the fuel tank and the area causing the leakage.

The pressure drop is considered to be linear for p> 20 hPa, since ρ _T remains unchanged for short times, ie measurement times, as used here.

According to a further alternative development, it is advantageously provided that the leakage area is determined by including an artificially generated fixed leakage area. In this way, can be dispensed with a level indicator in the fuel tank to determine the volume of fuel in the fuel tank (V _F ), and the process is cheaper.

wobei A_Fix die künstlich erzeugte Leckagefläche, deren Fläche bekannt ist, A_Leck die Leckagefläche des Kraftstoffbehälters, p₁ ein erster Druck in N/m², p₂ ein zweiter Druck in N/m² mit p₂ < p₁, R_s die spezifische Gaskonstante (287 (N*m)/(kg*K)), t₂ die Messzeit in Sekunden bei der Messung des Druckabfalls (p₁-p₂) über die Summe der Leckageflächen A_Fix+A_Leck, T die Temperatur im Kraftstoffbehälter in Kelvin, V_T1 das Luftvolumen im Kraftstoffbehälter in m³, ρ_T die Luftdichte im Kraftstoffbehälter in kg/m³ und v₂ die Luftströmungsgeschwindigkeit in m/s ist, wobei V_T1 mittels nachfolgender Gleichung (5) aus einer Messung des Druckabfalls (p₁-p₂) über die Leckagefläche A_Leck ermittelt wird: $${\text{V}}_{\text{T1}}=\left({\text{A}}_{\text{Leck}}*{\text{v}}_2*{\text{R}}_{\text{s}}*\text{T}*{\text{t}}_{\text{1}}*{\mathrm{\rho }}_{\text{T}}\right)/\left({\text{p}}_1-{\text{p}}_2\right)$$

wobei t₁ die Messzeit in Sekunden ist, die zur Messung des Druckabfalls (p₁-p₂) über die Leckagefläche A_Leck benötigt wird.In this case, the leakage area is determined by solving equation (4) below: $${\text{A}}_{\text{fix}}+{\text{A}}_{\text{leak}}=\left[\left({\text{p}}_1-{\text{p}}_2\right)*{\text{V}}_{\text{T1}}\right]/\left[{\text{v}}_2*{\text{t}}_2*{\text{R}}_{\text{s}}*\text{T *}{\mathrm{\rho }}_{\text{T}}\right]$$

where A _{Fix is} the artificially generated leakage area whose area is known A _leak the leakage area of the fuel tank, p ₁ a first pressure in N / m ² , p ₂ a second pressure in N / m ² with p ₂ <p ₁ , R _s the specific gas constant (287 (N * m) / (kg * K)), t ₂ the measuring time in seconds when measuring the pressure drop (p ₁ -p ₂ ) over the Sum of the leakage areas A _Fix + A _Leak , T the temperature in the fuel tank in Kelvin, V _T1 the volume of air in the fuel tank in m ³ , ρ _T the air density in the fuel tank in kg / m ³ and v ₂ the air flow velocity in m / s, where V _{T1 is determined} by means of the following equation (5) from a measurement of the pressure drop (p ₁ -p ₂ ) via the leakage area A _leak : $${\text{V}}_{\text{T1}}=\left({\text{A}}_{\text{leak}}*{\text{v}}_2*{\text{R}}_{\text{s}}*\text{T}*{\text{t}}_{\text{1}}*{\mathrm{\rho }}_{\text{T}}\right)/\left({\text{p}}_1-{\text{p}}_2\right)$$

where t _{1 is} the measuring time in seconds needed to measure the pressure drop (p ₁ -p ₂ ) across the _{leak area} A _leak .

To further simplify the process management is advantageously provided that the fixed leakage area is adjusted by means of a valve, since thus the fixed leakage area can be precisely specified.

list of figures

• 1 ein Diagramm zur Veranschaulichung von Druckabfallmessungen.

Hereinafter, an embodiment of the invention will be described in detail with reference to the accompanying drawings. In the drawing is:

• 1 a diagram illustrating pressure drop measurements.

Embodiment of the invention

In detail, the diagram of FIG 1 Five curves obtained from the measurement of pressure drop over time in a pressure range between 40 hPa and 20 hPa. Here, two different levels in the fuel tank ( 10 Liters and 60 liters) as well as different sized leakage areas (diameter = 0.5 mm, 0.8 mm, 1.0 mm). The leakage area is thus calculated according to: $${\text{A}}_{\text{leak}}={\text{D}}_{{\text{leak}}^2}/4*\mathrm{\pi };$$

With A = leakage area, D = leakage diameter and π = 3.14 = const.

In 1 curve A is a pressure drop curve using a 60L fuel tank and a leakage with a leakage diameter of 0.5 mm (leakage area = 0.196 mm ² ).

Curve B is a pressure drop curve using a 60L fuel tank and a leakage with a leakage diameter of 0.8 mm and a leakage area of 0.502 mm ² .

Curve C is a pressure drop curve using a 60L fuel tank and a leakage with a leakage diameter of 1.0 mm and a leakage area of 0.785 mm ² .

Curve D is a pressure drop curve using a 10L fuel tank and a leakage with a leakage diameter of 0.5 mm and a leakage area of 0.196 mm ² .

Curve E is a pressure drop curve using a 10L fuel tank and a leakage with a leakage diameter of 0.8 mm and a leakage area of 0.502 mm ² .

Curve F is a pressure drop curve using a 10L fuel tank and a leakage with a leakage diameter of 1.0 mm and a leakage area of 0.785 mm ² .

The following example shows the determination of a leakage area according to two methods:

Method 1)

• p₁= 40 hPa=4000Pa (N/m²)
• p₂= 20 hPa=2000Pa (N/m²)
• p_a= 998 hPa=99800Pa (N/m²)
• V_T= 100 L
• V_F= 40 L
• V_T1= V_T-V_F = 60 L = 0,06 m³
• R_s=287 (N*m)/(kg*K)
• T =273 K (0°C ; ohne Ausgasungskorrektur an ρ_T)
• ρ_a=1,2 Kg/m³
• ρ_T =1,2 Kg/m³
• t =63s

The following values were assumed, whereby the fuel volume of the fuel tank was determined via a fuel gauge.

• p ₁ = 40 hPa = 4000 Pa (N / m ² )
• p ₂ = 20 hPa = 2000 Pa (N / m ² )
• p _a = 998 hPa = 99800 Pa (N / m ² )
• V _T = 100 L
• V _F = 40 L
• V _T1 = V _T -V _F = 60 L = 0.06 m ³
• R _s = 287 (N * m) / (kg * K)
• T = 273 K (0 ° C, without outgassing correction on ρ _T )
• ρ _a = 1.2 Kg / m ³
• ρ _T = 1.2 kg / m ³
• t = 63s

From formula (2) results: $${\text{v}}_{\text{2}}=\surd \left[2*\left({\text{p}}_{\text{t}}-{\text{p}}_{\text{a}}\right)/{\mathrm{\rho }}_{\text{a}}\right]\to {\text{v}}_2=\surd \left[2*\left({\text{p}}_{\text{t}}-{\text{p}}_{\text{a}}\right)/{\mathrm{\rho }}_{\text{a}}\right]=70.71\text{m / s}$$

Substituted in formula (1): $$\begin{array}{l}{\text{A}}_{\text{leak}}=\left[\left({\text{p}}_1-{\text{p}}_{\text{2}}\right)*{\text{V}}_{\text{T1}}\right]/\left({\text{v}}_2*{\text{R}}_{\text{s}}*\text{T}*\text{t}*{\mathrm{\rho }}_{\text{T}}\right)=\hfill \\ \left[2000{\text{N / m}}^2*0.06{\text{m}}^3\right]/70.71\text{m / s * 287hPa}*\text{273K}*63\text{s}*1.2{\text{kg / m}}^{\text{3}}=\hfill \\ \left(0.412\right)*\left(10*\text{exp}-6\right){\text{m}}^2=0.29{\text{mm}}^2\hfill \end{array}$$

This results in a leakage diameter of 0.6 mm according to: $${\text{D}}_{\text{leak}}=\surd 4*{\text{A}}_{\text{leak}}/\pi =\surd 4*0.29{\text{mm}}^2/3.14=0.607\text{mm}$$

Method 2)

The following values were assumed, with the fuel tank fuel volume unknown.

• p₁= 40 hPa=4000Pa (N/m²)
• p₂= 20 hPa=2000Pa (N/m²)
• p_a= 998 hPa=99800Pa (N/m²)
• R_s=287 N*m/kg*K
• T =273 °K (0°C ; ohne Ausgasungskorrektur an ρ_T)
• ρ_a=1,2 Kg/m³
• ρ_T=1,2 Kg/m³
• t₂=60s
• t₁=145s (in Formel 5 als
• A_Fix=0,196 mm² (für z.B. einen Leckagedurchmesser von 0,5 mm)

First, the time t ₁ required for the pressure drop from p ₁ to p _{2 was} measured, and then a known, fixed leakage (here: 0.5 mm diameter (this corresponds to a leakage area of 0.196 mm ² ) was switched on. This results in the second time for the summed leaks, t ₂ .

• p ₁ = 40 hPa = 4000 Pa (N / m ² )
• p ₂ = 20 hPa = 2000 Pa (N / m ² )
• p _a = 998 hPa = 99800 Pa (N / m ² )
• R _s = 287 N * m / kg * K
• T = 273 ° K (0 ° C, without outgassing correction on ρ _T )
• ρ _a = 1.2 Kg / m ³
• ρ _T = 1.2 kg / m ³
• t ₂ = 60s
• t ₁ = 145s (in formula 5 as
• A _Fix = 0.196 mm ² (for eg a leakage diameter of 0.5 mm)

From formula (2) results: $${\text{v}}_2=\surd \left[2*\left({\text{p}}_{\text{t}}-{\text{p}}_{\text{a}}\right)/{\mathrm{\rho }}_{\text{a}}\right]=70.71\text{m / s}$$

Inserted in formula (1): $$\begin{array}{l}{\text{A}}_{\text{leak}}+{\text{A}}_{\text{fix}}=\left[\left({\text{p}}_1-{\text{p}}_2\right)*{\text{V}}_{\text{T1}}\right]/\left({\text{v}}_2*{\text{R}}_{\text{s}}*\text{T}*{\text{t}}_2*{\mathrm{\rho }}_{\text{T}}\right)\hfill \\ {\text{A}}_{\text{leak}}=\left[\left({\text{p}}_1-{\text{p}}_{\text{2}}\right)*{\text{V}}_{\text{T1}}\right]/\left({\text{v}}_2*{\text{R}}_{\text{s}}*\text{T}*\text{t}1*{\mathrm{\rho }}_{\text{T}}\right)\hfill \\ {\text{A}}_{\text{leak}}={\text{A}}_{\text{fix}}*({\text{t}}_2/\left({\text{t}}_1-{\text{t}}_2\right)\hfill \\ {\text{A}}_{\text{leak}}=0.196{\text{mm}}^2*0.705=0.138{\text{mm}}^2\hfill \end{array}$$

$${\text{D}}_{\text{Leck}}=\surd 4*\mathrm{0,138}{\text{ mm}}^2/\mathrm{3,14}=\mathrm{0,419}\text{ mm}$$

This results in a leakage diameter of 0.41 mm according to: $${\text{D}}_{\text{leak}}=\surd 4*{\text{A}}_{\text{leak}}/\pi$$

$${\text{D}}_{\text{leak}}=\surd 4*0.138{\text{mm}}^2/3.14=0.419\text{mm}$$

$$\begin{array}{l}{\text{V}}_{\text{T1}}=(\mathrm{0,138}{\text{ mm}}^2*\left(10\text{*exp}-6\right)\hfill \\ *\mathrm{70,71}\text{m}/\text{s}*\text{287hPa}*\text{273K}*\text{145s}*\text{1}\text{,2kg}/{\text{m}}^3/2000{\text{N/mm}}^2=\mathrm{0,066}{\text{ m}}^3=\hfill \\ 66\text{ L}\hfill \end{array}$$

From formula (5): $${\text{V}}_{\text{T1}}=\left({\text{A}}_{\text{leak}}*{\text{v}}_2*{\text{R}}_{\text{s}}*\text{T}*{\text{t}}_1*{\mathrm{\rho }}_{\text{T}}\right)/\left({\text{p}}_1-{\text{p}}_2\right)$$

$$\begin{array}{l}{\text{V}}_{\text{T1}}=(0.138{\text{mm}}^2*\left(10\text{* exp}-6\right)\hfill \\ *70.71\text{m}/\text{s}*\text{287hPa}*\text{273K}*\text{145s}*\text{1}\text{, 2kg}/{\text{m}}^3/2000{\text{N / mm}}^2=0.066{\text{m}}^3=\hfill \\ 66\text{L}\hfill \end{array}$$

This shows that e.g. for a fuel tank volume of 100L still 34 L of fuel are available.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• DE 102013012881 A1 [0002]

Claims (6)

Method for determining a leakage area A _{leak of} a fuel tank, comprising the steps: - pressure build-up under pressure generation in the fuel tank, - measurement of a pressure drop over a measuring time (t) and - determination of the leakage area A _leak . Method according to Claim 1 , characterized in that the pressure build-up is carried out by means of a volume flow pump. Method according to one of the preceding claims, characterized in that the leakage area A _{leak is} determined by solving the following equation (1): $${\text{A}}_{\text{leak}}=\left[\left({\text{p}}_1-{\text{p}}_2\right)*{\text{V}}_{\text{T1}}\right]/\left({\text{v}}_2*{\text{R}}_{\text{s}}*\text{T}*\text{t}*{\mathrm{\rho }}_{\text{T}}\right)$$

wherein in equation (1) A _leak quantifies the leakage area to be determined, p ₁ a first pressure in N / m ² , p ₂ a second pressure in N / m ² with p ₂ <p ₁ , ρ _T the air density in the fuel tank in kg / m ³ , R _{s is} the specific gas constant (287 (N * m) / (kg * K)), t is the measurement time in seconds when measuring the pressure drop (p ₁ -p ₂ ), T is the temperature in the fuel tank in Kelvin, V _{T1 is} the volume of air in the fuel tank in m ³ and v _{2 is} the air flow velocity in m / s, with $${\text{v}}_2=\surd \left[2*\left({\text{p}}_{\text{t}}-{\text{p}}_{\text{a}}\right)/{\mathrm{\rho }}_{\text{a}}\right]$$

where p _t denotes an average in N / m ² between p ₁ and p ₂ and p _a denotes the atmospheric pressure in hPa, where p _t and p _a are determined via pressure sensors; and ρ _{a is} the air density in the vicinity of the fuel tank in kg / m ³ , and $${\text{V}}_{\text{T1}}={\text{V}}_{\text{T}}-{\text{V}}_{\text{F}}$$

where V _{T is} the volume of the fuel tank in m ³ and V _{F is} the volume of fuel in the fuel tank in m ³ , and V _{F is determined} from a tank level gauge. Method according to Claim 1 or 2 , characterized in that the leakage area A _leak including an artificially generated fixed leakage area A _F i _x , is determined. Method according to Claim 4 , characterized in that the leakage area A _{leak is} determined by solving the following equation (4): $${\text{A}}_{\text{fix}}+{\text{A}}_{\text{leak}}=\left[\left({\text{p}}_1-{\text{p}}_2\right)*{\text{V}}_{\text{T1}}\right]/\left({\text{v}}_2*{\text{t}}_2*{\text{R}}_{\text{s}}*\text{T}*{\mathrm{\rho }}_{\text{T}}\right)$$

A _fix the artificially created leakage area, A _leak the leakage area of the fuel tank, p ₁ a first pressure in N / m ² , p ₂ a second pressure in N / m ² with p ₂ <p ₁ , R _s the specific gas constant (287 (N * m) / (kg * K)), t ₂ the measuring time in seconds when measuring the pressure drop (p ₁ -p ₂ ) over the sum of the leakage areas A _Fix + A _leak , T the temperature in the fuel tank in Kelvin, V _{T1 is} the volume of air in the fuel tank in m ³ , ρ _{T is} the air density in the fuel tank in kg / m ³ and v _{2 is} the air flow velocity in m / s, where V _{T1 is calculated} from the pressure drop (p ₁ ) by equation (5) below. p ₂ ) is determined via the leakage area A _leak : $${\text{V}}_{\text{T1}}=\left({\text{A}}_{\text{leak}}*{\text{v}}_2*{\text{R}}_{\text{s}}*\text{T}*{\text{t}}_1*{\mathrm{\rho }}_{\text{T}}\right)/\left[\left({\text{p}}_{\text{1}}*{\text{p}}_2\right)\right]$$

where t _{1 is} the measuring time needed to measure the pressure drop (p ₁ -p ₂ ) across the leakage area A _leak . Method according to Claim 4 or 5 , characterized in that the fixed leakage surface A _{Fix is} adjusted by means of a valve.

Images